How to Make It
Preheat the oven to 375°. In a bowl, whisk the egg yolks with the lemon juice and garlic. Very gradually whisk in drops of the vegetable oil until starting to thicken, then gradually whisk in the remaining vegetable oil and 1/2 cup of the olive oil until thick. Season with salt and pepper.
Bake the closed hoagie rolls for 3 minutes, until warm. Spread the aioli on the cut sides. Top the bottom halves with the peppers, meats and cheese. Bake for 5 minutes, until the cheese melts. Top with the tomatoes and oregano and season with salt and pepper. Pile the lettuce on top, drizzle on the vinegar and remaining 1/4 cup of olive oil and serve.