Preheat oven to 375 degrees Fahrenheit.
Line 2 baking sheets with parchment paper and set aside.
Slice eggplants into 1/3" thick slices, place in colander, and generously salt. Set aside for 5-7 minutes.
Meanwhile, mix up olive oil, balsamic vinegar, oregano, garlic, salt and pepper in a small mixing bowl.
Wipe down eggplant slices with a paper towel to remove moisture and salt. Arrange eggplant slices in a single layer on baking sheets.
Brush marinade over both sides of each eggplant slice. Bake for 40-45 minutes or until eggplant is fork tender. Flip slices over after 20 minutes of baking and brush with additional olive oil if needed.
While eggplant is baking, add olive oil to a large skillet or enamel cast iron oven. Add peppers and onions and sauté over medium-high heat until tender. Stir in garlic, salt and pepper and cook until completely softened and moisture has cooked off, about 25-30 minutes.
To make the tzatziki sauce, grate cucumber onto a cutting board and then transfer to a strainer and gently squeeze some of the moisture out of it. Transfer to a small mixing bowl and add the rest of the ingredients then stir to combine.
Assemble sandwiches by adding 2-3 eggplant slices, 1/4 peppers, 2-3 tablespoons tzatziki, and other toppings as desired.