Preheat the oven to 375°F (190°C) and spray a 9x13-inch casserole dish with nonstick spray or lightly brush with 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 roughly 1 1/2 cups, about 10 minutes; stir occasionally to prevent scorching.
While the salsa reduces, trim any excess fat from the chicken breasts and make their thickness similar by trimming or gently pounding as needed.
Mix the ground cumin, garlic powder, onion powder, salt, and black pepper in a small bowl, then rub the spice mix over both sides of each chicken breast.
Heat 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Brown the seasoned chicken about 2–3 minutes per side until just golden but not cooked through.
Transfer the browned 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 as needed.
Pour the reduced salsa verde evenly over the chicken strips.
Sprinkle the 2 cups of grated mozzarella evenly over the sauced chicken.
Bake in the preheated oven for 25–30 minutes, until the casserole is bubbling, the cheese is melted and lightly browned, and the chicken is cooked through (internal temperature 165°F / 74°C).
Let rest a few minutes, then serve hot.
