Place a large cast iron skillet in the oven. Preheat the oven to 450 degrees F (230 degrees C).
Toss green beans, 1/2 tablespoon butter, 1/2 teaspoon salt, and 1/4 teaspoon pepper in the hot skillet. Return to the oven and roast for 3 minutes.
Meanwhile, sprinkle remaining 1/2 teaspoon salt and 1/4 teaspoon pepper over tilapia fillets.
Combine bread crumbs, almonds, and sage in a small bowl; stir in remaining 1 1/2 tablespoon butter. Sprinkle enough topping over the tilapia to cover the surface. Press topping lightly to adhere.
Carefully remove skillet from the oven. Sprinkle remaining topping over the green beans and toss lightly. Place the tilapia on top, in the center of the skillet.
Roast until flesh flakes easily with a fork, 10 to 13 minutes.
