Turkey, apple, and havarti on toast or a criossant. Mayo and spinach for decoration. Named 'What can Brown do for you?' 

The Kottke is an amazing name for a sandwich. I also used to do a tuna salad mix with pickles, pickle juice and scallions. Harvati is a great addition I hadn't considered, might have to give that a go.

My go to sandwich, when I don't mind the calories, is a pastrami Rachel - pastrami, Swiss cheese, cole slaw, and Russian dressing on Sissel (light rye) or marble rye - preferably grilled. The preferred pairing is a regular coke with pearl/pebble ice cubes. 

If a named sandwich must be unique in some way, I'd swap out the mayo based slaw for a vinegary slaw, like the ones in a banh mi, and maybe add tomato. Maybe as a nod to Rachel from "Friends," you could call it "The One with the Banh Mi Slaw".

This is the reverse but before our local general store got all upscaled, they had a sandwich called the "Foxy Lady" and I always felt special when I ordered it. And foxy!

Toasted everything bagel with plain or other savory cream cheese on the bottom and dijon mustard on the top, cucumber, flavorful tomato slices (so in winter, only sliced cherry tomatoes), spinach or arugula, a fried egg, and sharp cheddar.

(Yes I know that good bagels don't need to be toasted. But they must in this case.)

Mine would be seasonal as it relies heavily on home grown tomatoes, specifically the big ones - giant slicers - a mortgage lifter or maybe an early girl, sliced very thick, seasoned with salt and fresh pepper, a liberal spread of Best Foods or Duke's, on good, lightly toasted white bread, cut on the diagonal, and preferably eaten while standing over the sink. 

Fried egg on fluffy white bread, mayo, liberal shake of italian seasoning, and fat slice of tomato.

The bread is "Korngeflüster" (whispering wheat), very dark, from a local bakery, topped with my homemade herb butter, Gorgonzola, honey, jalapeños, pickled onions and Maldon salt

Hear me out: a Reuben but with kimchi. 

Also, a grilled cheese with broccoli added to it.

At my college co-op, my standard order was turkey with cheddar and jack grilled (as in, they would put a slice of turkey straight onto the flat top, add cheese on top of it, put another piece of turkey on top of that, and grill it together into a kind of delicious meat and cheese packet) all on toasted sourdough with avocado, mayo, and sprouts. Perfect late-night study food. 

My go to lately has been smoked ham, hummus, and sauerkraut. Usually on toasted sourdough, or a nice fluffy flatbread. 

The world's best tuna-melt - homemade sourdough bread grilled in a cast-iron skillet with mayo instead of oil. Then melted Havarti cheese, chopped green onions, and albacore tuna salad with kalamata olive spread.

They sell a version of it in Corvallis, Oregon. So if you ever visit Oregon State University, head downtown and grab lunch!

A slight variation on an Italian veggie, that I get all the time. Roasted red peppers, basil, fresh mozzarella, Italian spices, olive oil (that's the standard Italian veggie),  add Molinari's salami (the variation). Because I'm from San Francisco, it's on Dutch Crunch. 

Not to take this thread in a different direction but all of these interesting sandwiches made me think of having a sandwich that was unexpectedly delicious. A local grocery store had a sandwich for few months that was the following:

Soft Demi Baguette (nothing special)
Deli Turkey
Pickled Jalapeño
Sliced Pear (I dare say of the canned variety)
Arugula
Mayo/dijon

Salty, Savoury, slightly sweet, spicy, peppery from the arugula. I may have been the only fan since they no longer sell it.

My grandpa always had two PBB (Peanut Butter & Bacon) sandwiches for his night watch shift.  I'd occasionally get a half. You'd probably have to name it "the grandpa". Makes any day just a bit better :)

1. A much better burger: mix ground beef and ground pork, and put that badboy on an english muffin bun.

2. Carved turkey with mayo and cran on a baguette.

3. Polish sausage with cream cheese on a toasted french roll.

When she was little (before discovering jamon with comte or brie and butter on baguette) my older daughter hated sandwiches. She loved soup, especially lentil. So I made her a "lentil soup sandwich" which was basically a pile of lentils on whole wheat sourdough. We laughed about that for a long time... 

Though it's been on the regular menu for some time, back when they opened, Cutty's (https://www.cuttyfoods.com) only had a Roast Beef 1000, and I believe my wife and I were some of the first people to regularly sub turkey to make a Turkey 1000. As well, we always have them add chard to the sandwich... So a Turkey 1000 with chard (roast turkey, crispy shallots, sharp cheddar, garlicky sauteed chard, 1000 island dressing, on black pepper brioche).