Preheat oven to 400 F and cut off the very top of a head of garlic. Drizzle with a little olive oil and loosely wrap in foil. Set directly on an oven rack and bake for 45 minutes.

Meanwhile, caramelize the onions by heating 2 tbsp olive oil in a large skillet over medium low heat. Once hot, add the sliced onion. Cook over medium low heat, stirring occasionally, until golden brown and very soft, about 30 minutes. Remove onions from skillet and set aside. Leave the pan on the stove (but remove from the heat) to cook the mushrooms later.

Meanwhile, use a damp washcloth or paper towel to clean the mushrooms by wiping away any dirt and removing the stems. Place on a plate or sheet pan and set aside.

To a small mixing bowl, add olive oil, balsamic vinegar, basil, oregano, salt, and pepper. Whisk to combine, then pour the marinade over both sides of the mushrooms, using a pastry brush to distribute evenly. Return the mushrooms to the plate, stem-side-up, and set aside at room temperature.

When the garlic is done and cooled enough to handle, combine the mayonnaise, roasted garlic cloves (squeeze them out from the base up), 1/2 tsp of salt, and 1/2 tsp of freshly ground black pepper in a blender. Blend on high until smooth, scraping down sides as needed. Taste and adjust seasonings as needed.

Return the skillet to the stovetop over medium high heat. Once hot, add portobello mushrooms and sauté for 2-4 minutes on each side, or until the mushrooms are deep golden brown on the edges and slightly softened. While cooking, brush with any leftover marinade for extra flavor.

Meanwhile, prepare any serving items, such as toasting hamburger buns or chopping greens.

To serve, add a generous spoonful of garlic aioli to the inside of each bun. On the bottom bun, stack a portobello mushroom, caramelized onions, lettuce, and roasted red peppers.

Enjoy immediately. Store leftover mushrooms and separately in the refrigerator up to 2-3 days, though best when fresh. Aioli will keep in the refrigerator for 7-10 days.