This Aioli is very creamy, a little spicy and is made with-out eggs, because avocado has enough fat and body for an emulsion.
It can be served with a wide variety of sandwiches or as a sauce for fish, meat and vegetable dishes or just as a dip for chips like a guacamole.
I think it would be even more piquant if the roasted peppers were in a marinade or instead of peppers to cut a few Sun-Dried tomatoes.
Heat 1/2 tablespoon oil in a large skillet over medium heat. Cook onion until translucent, about 4 minutes. Add mushrooms and cook stirring about 10 minutes, season with salt and pepper. Let cool slightly.
Transfer to a food processor and pulse 3-4 times until coarsely chopped.
Add remaining ½ tablespoon of oil to skillet and heat over high heat. Add leeks, season with salt and pepper and cook stirring until leeks are tender, 5to 6 minutes.
Add mushroom mixture to skillet and stir to combine. Remove from heat and add vinegar; stir to combine. Transfer to a bowl and let cool to room temperature before using.
Peel and cut avocados and roasted peppers in about ¼- inch pieces, transfer to a food processor.
Add Mascarpone, garlic, cayenne pepper, 1 teaspoon lime juice and 1 tablespoon oil.
Process, to start the emulsion; then continue alternating 1 a teaspoon of lime juice and a few drops of oil at a time.
Repeat until all of the lime juice and oil are incorporated and the Aioli thickens. Season with salt and pepper, mix-in cilantro and process briefly, just to combine. Transfer to a jar and chill.
To serve preheat broiler. Slice baguette in half lengthwise and place on a baking sheet cut-side up, drizzle cut sides with a little olive oil.
Transfer baking sheet to broiler and broil until tops are toasted, 2 to 3 minutes. Let bread cool to room temperature. Divide the mushroom and leek mixture in half, spread baguette halves and spread to cover.
Top each half with a generous drizzle of the Avocado and Red Pepper Aioli.