Preheat the oven to 375°F (190°C) and lightly grease a 9x13-inch (or similar) casserole dish with nonstick spray or olive oil.
Pour the 16 oz jar of salsa verde into a small saucepan and simmer over low heat until reduced by about one-fourth to approximately 1½ cups, about 10 minutes; this prevents the casserole from becoming watery.
While the salsa reduces, trim each chicken breast so the pieces are similar in size and thickness; optionally pound to even thickness.
Mix the ground cumin, garlic powder, onion powder, salt, and fresh-ground black pepper. Rub the spice mixture onto both sides of each chicken breast.
Heat 1 tablespoon olive oil in a large nonstick frying pan over medium-high heat. Brown the chicken breasts 2–3 minutes per side until lightly browned but not cooked through.
Remove the chicken to a cutting board and cut each breast into three lengthwise strips.
Arrange the chicken strips crosswise in the prepared casserole dish, staggering to fit.
Pour the reduced salsa verde evenly over the chicken strips.
Sprinkle the 2 cups grated mozzarella evenly over the salsa-covered chicken.
Bake in the preheated oven for 25–30 minutes, until the casserole is bubbly, the cheese is melted and browned, and the chicken is cooked through.
Let the dish rest briefly, then serve hot.