4 slices Italian bread (1 inch thick), lightly toasted
1/2 cup sandwich giardiniera, drained and finely chopped
4 thin slices tomato
Minced fresh parsley
For aioli, in a small bowl, combine the mayonnaise, olive oil, garlic, salt and pepper; set aside.
Sprinkle Parmesan into large nonstick skillet; heat over medium heat. Cook just until melted, about 2 minutes. Break eggs, 1 at a time, into a custard cup or saucer, then gently slide into pan over Parmesan. Immediately reduce heat to low. To prepare eggs sunny-side up, cover pan and cook until yolks thicken but are not hard, 4-5 minutes.
Spread aioli over toasted bread. Top with giardiniera, tomato and egg. Sprinkle with parsley.