Preheat the oven to 425°F (220°C) and line a small baking sheet with aluminum foil.
In a bowl, toss the trimmed green beans with 2 tablespoons olive oil, 1/2 teaspoon garlic salt, and 2 tablespoons Italian panko breadcrumbs until evenly coated.
Push the green beans to one side of the prepared baking sheet to make room for the chicken.
Pat the chicken breasts dry with paper towels and season both sides with salt and pepper to taste.
Place the chicken breasts on the empty side of the baking sheet.
Spread 1 tablespoon sun-dried tomato pesto over each chicken breast, then top each with one slice of mozzarella.
Bake in the preheated oven for about 25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C).
If desired, broil for 3–5 minutes at the end to brown the cheese; watch closely to avoid burning.