How to Make It
In a food processor, pulse the egg yolks, lemon juice, vinegar, mustard and garlic to blend. With the machine on, slowly drizzle in the oil until incorporated. Season with salt and pepper.
Preheat the oven to 375°. Spread one side of each bread slice with 1/2 tablespoon of the butter. Arrange buttered side up on a baking sheet and toast until golden, 6 to 8 minutes. Top 4 of the toasts with the brie, sauerkraut and mortadella.
In a small bowl, mix 1/4 cup of the aioli with the mustard. Spread the mustard aioli on the remaining 4 toasts and close the sandwiches. Bake until the mortadella is warm and the brie is melted, 8 to 10 minutes. Serve with pickles and extra lemon aioli.