In a small bowl, whisk together the pesto and mayonnaise.
Spread half of the butter on 1 side of each bread slice. Spread half of the pesto-mayo mixture on the unbuttered side of each bread slice.
Transfer 1 slice of bread in skillet, buttered side down. Top with 1 slice provolone, the tomato, turkey, ending with the remaining Provolone. Place second bread slice on top, buttered side up.
Cook, flipping once carefully, until both sides of bread are golden brown and cheese has melted, about 4 minutes per side, pressing down with a spatula after the first flip so both sides develop a crust.
(Give your bread a quick peek underneath from time to time to make sure it's not browning too quickly. If so, adjust your heat.)
Nutritional information given is an automatic calculation and can vary based on the exact products you use and any changes you make to the recipe. If these numbers are very important to you, I would recommend calculating them yourself.
Keyword: best grilled cheese, grilled cheese recipe, pesto grilled cheese