Whisk the vinegar and olive oil together in a small bowl and season with salt and pepper.
Slice the focaccia into 4 equal pieces; then slice each piece horizontally for sandwiches. Spread some of the Dijon mustard on the cut side of the bottom half of each focaccia. Top bread evenly with turkey, peppers, and season with salt and pepper. Add mozzarella and baby greens, and drizzle the balsamic dressing on top. Smear the top half of each focaccia with Key Lime Garlic Mayonnaise, and place on top of greens to finish sandwich. Brush the tops and bottoms of each sandwich with olive oil.
Heat a sandwich press, or use cast iron pans and aluminum foil covered bricks to press sandwiches. Cook the sandwiches, in batches if needed, until the cheese melts and the bread is toasted. Serve.
This recipe was provided by professional chefs and has been scaled down from a bulk recipe provided by a restaurant. The Food Network Kitchens chefs have not tested this recipe, in the proportions indicated, and therefore, we cannot make any representation as to the results.
Special Equipment: deep heavy-bottomed pot for frying turkey
Process the garlic, herbs, lemon zest, salt and pepper in a food processor fitted with the metal blade until coarsely ground. Rub mixture generously over turkey breast. Roll the turkey breast into a compact shape by turning the smaller end of the breast under. Wrap tightly in 3 layers of heavy-duty aluminum foil.
Fill a deep heavy-bottomed pot 2/3's full with oil. Heat over medium-high until a deep-fry thermometer reads 350 degrees F. Fry the turkey breast, wrapped in the foil, for 35 minutes or 12 minutes per pound. Carefully remove turkey from oil and set aside, wrapped in the foil, to cool to room temperature. Refrigerate turkey until firm enough to thinly slice, at least 2 hours or overnight.
Pulse the egg, mustard, garlic and lime juice in a food processor fitted with a metal blade. Season with salt and pepper, to taste. With the machine running, add the oil in a steady stream until the mixture is pale in color and thick. Transfer mayonnaise to a bowl, stir in zest, cover and refrigerate for 1 hour.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.