Frico is fried cheese. YUM. In this recipe, eggs cooked on top of crispy Parm sit on a toasted-bread salad. Be sure to toast the bread to bring out the nutty flavor.
Preheat the oven to 400°. On a rimmed baking sheet, arrange the bread in an even layer. Toast, turning once, until deep golden and nutty, about 15 minutes.
Meanwhile, for the dressing, in a medium bowl, mix the lemon juice, vinegar, shallot, and garlic; season with salt and pepper. Let marinate for 10 to 15 minutes. Place the cut sides of the tomato halves against the coarse side of a box grater and grate into the bowl; discard the skins. Whisk in the oil and sugar; season.
Arrange half the bread and the onion in the bottom of a shallow bowl. Pour half the dressing on top. Top with the tomato wedges, cucumber, and herbs. Let marinate for a few minutes.
While the bread marinates, heat a small (6-inch) nonstick skillet over medium. Evenly scatter 1/2 cup cheese on the bottom of the skillet. When it begins to bubble (1 to 2 minutes), crack an egg on top. Cover with a lid or foil and cook the egg until the white is set, about 2 minutes. Transfer to a plate. Repeat with the remaining cheese and eggs.
Top the salad with the remaining bread and dressing. Toss and season. Divide among plates. Top each with a frico egg.