Place the ground beef/fish/chicken, roast onions in a large bowl and add the mustard, olive oil, oregano, garlic, parsley, panko, egg, Worcestershire salt, and pepper.
Mix gently with a fork to combine, taking care not to compress the ingredients. Shape the meat into 2 (2-inch) patties of equal size and thickness
In a food processor, puree the egg yolks and garlic. Add the ground peppercorns with the motor running; slowly drizzle in the olive oil until the sauce is emulsified.
After the sauce is completely emulsified, thin it with 1 teaspoon of water at a time. Season the sauce to taste with salt and lemon juice.
Heat olive oil and butter in a large skillet over medium heat; cook and stir onions and sugar in hot oil until onions start to caramelize, about 15 minutes. Stir red wine and balsamic vinegar into onion mixture and bring to a boil. Reduce heat to medium-low and simmer until liquid is evaporated, 15 to 20 minutes more. Season with salt
When the grill is medium-hot, brush the grill grate with oil to keep the sliders from sticking. Place the sliders on the grill and cook for 4 minutes.
Turn the sliders over with a spatula and cook for another 4 to 6 minutes, until medium-rare, or cook longer if you prefer the sliders better done. Slice the buns in half crosswise spread butter and toast the halves cut side down on the grill.
Divide the lettuce among the 2 bottom buns, top each with a tomato slice and slider, and finish with caramelized onion. Cover with the top of the bun and serve hot with black pepper aioli and condiments.