Heat 2 tablespoons of the oil in a large sauté pan over medium heat, toss in the garlic, onion, mushrooms, and bell peppers, and sauté until softened, about 5 minutes. Remove from the heat, and set aside in the refrigerator to chill.
Stir together the eggs, pasta, cheese, thyme, basic, oregano, and chilled sautéed vegetables in a large bowl, and season with salt and pepper. Heat the butter and remaining oil in a small sauté or omelet pan over medium-high heat, and add about one-quarter of the egg mixture, shaping it into a cake about 1 inch thick and 3 inches in diameter. Brown on each side for about 5 minutes, then remove the frittata to a covered plate to keep warm. Repeat three more times with the remaining mixture.
In a small mixing bowl, stir together the mayonnaise and mustard.
To serve, set each frittata in the center of a plate, place a dollop of the mayonnaise mixture on top. Roll the prosciutto into rosettes and place on top. Garnish with chives.
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