Turn oven on to 450 degrees. Let preheat, at least 10 minutes.
Remove all produce from any packaging or constraints, then thoroughly rinse and pat dry.
Prepare a baking sheet with foil and cooking spray.
Quarter potato lengthwise. Cut into ½" pieces. Place on prepared baking sheet and toss with 1 tsp. olive oil, ½ tsp. salt, and a pinch of pepper. Spread into a single layer. Roast 20 minutes. Potatoes will finish cooking in a later step. While potatoes roast, halve and peel onion. Cut halves into ¼" slices. Mince garlic and combine with 1 tsp. olive oil. Core tomato and cut into ¼" slices.
Combine half the pesto (reserve remaining for mozzarella) and mayonnaise in a mixing bowl. Combine remaining pesto and mozzarella in another mixing bowl. Form ground beef into four equal-sized patties (about ½" thick and 4" in diameter). Divide mozzarella-pesto mix between the middle of two burger patties. Place remaining patties on cheese-topped patties and seal edges by pinching lightly.
Place a medium non-stick pan over medium heat and add 2 tsp. olive oil. Add onions to hot pan and stir occasionally until tender, 5-7 minutes. Add balsamic vinegar and stir occasionally, 1-2 minutes. Remove from burner. Transfer onions to a plate. Wipe pan clean and reserve. While onions cook, halve buns, if necessary. Place cut side down directly on oven rack and toast until lightly browned, 2-3 minutes.
After potatoes have roasted 20 minutes, drizzle with garlic-oil mixture. Roast until garlic is fragrant and potatoes are lightly browned, 5 minutes. While potatoes roast, return pan used to cook onions to medium heat and add 2 tsp. olive oil. Add burgers to hot pan and cook until burgers reach a minimum internal temperature of 160 degrees, 5-6 minutes per side. Remove from burner.
Plate dish as pictured on front of card, garnishing with sauce, onion, and tomato. Bon appétit!
