Place the broccoli in a microwave-safe dish with 2 tablespoons of water, cover with plastic wrap, and microwave for 1 minute until tender. Drain any remaining water thoroughly, then transfer to a mixing bowl. Add the finely diced bell pepper, shredded cheddar cheese, mayonnaise, 1/2 teaspoon garlic powder, 1/4 teaspoon onion powder, and a pinch of salt and black pepper. Mix well until the filling is evenly combined. Set aside while you prepare the chicken.

Pat the chicken breasts dry with paper towels to ensure proper browning later. Season both sides generously with salt, black pepper, 3/4 teaspoon garlic powder, and paprika. Lay each breast flat on a cutting board and carefully cut a pocket horizontally into the thickest part of each breast, being careful not to cut all the way through—you want to create a pocket that opens from one side. I like to gently feel for the thickest part first to make sure I'm cutting in the right spot for even cooking.

Preheat your oven to 425°F. Divide the broccoli and cheese filling from Step 1 evenly among the four chicken pockets, being careful not to overstuff—you want the filling to stay inside during cooking. Heat 2 tablespoons of olive oil in a large oven-safe skillet over medium-high heat until shimmering. Once hot, carefully place the stuffed chicken breasts in the skillet and sear for 3-4 minutes per side until golden brown. Don't move them around too much—let each side develop a nice crust for better flavor.

Cover the skillet tightly with aluminum foil to trap steam and help the chicken cook through evenly. Transfer the skillet to the preheated 425°F oven and bake for 15-17 minutes, until the internal temperature reaches 165°F when measured with a meat thermometer at the thickest part of the largest breast. Let the chicken rest in the skillet for 5 minutes before serving—this allows the juices to redistribute, keeping the meat tender and moist inside.