Season chicken with salt and pepper. Melt 1 tbsp butter in a large skillet over medium-high heat. Brown chicken on both sides, about 4 to 5 minutes, and transfer to a plate.

Add spinach to the same skillet and cook over medium heat, stirring, until just wilted, about 2 minutes. Scoop into a colander and press out as much liquid as possible. Squeeze again with your hands once cool.

Melt remaining 2 tbsp butter in the skillet over medium heat. Add garlic and cook 30 seconds. Whisk in flour and cook 1 minute. Slowly whisk in milk, simmer until thickened, about 3 minutes. Turn heat to low, stir in cream cheese, Parmesan, ½ tsp salt, ¼ tsp pepper, and red pepper flakes until smooth.

Preheat oven to 375°F (190°C). In a 9x13-inch baking dish, spread artichoke hearts and spinach evenly across the bottom. Top with chicken, pour sauce over everything, and sprinkle mozzarella on top.

Bake for 25 to 30 minutes until bubbly and golden on top. Broil the last 1 to 2 minutes if you want a deeper brown.

Let the casserole rest for 5 minutes, then scoop onto plates and serve hot.