Preheat your oven to 375°F (190°C). Lightly grease a baking dish or line it with parchment for easy cleanup.
Use a sharp knife to carefully slice a pocket into the side of each chicken breast. You don’t want to cut all the way through—just a deep crease to hold the filling.
In a small bowl, mix together the steamed broccoli, shredded cheddar, cream cheese, and minced garlic. Add salt, pepper, paprika, and thyme if you’re using them. Stir until the filling looks cohesive and a bit glossy.
Stuff each chicken pocket with about 1/4 of the filling. If needed, secure with toothpicks to keep the filling inside while it bakes.
Heat olive oil in a skillet over medium heat. Sear the stuffed chicken for 2-3 minutes per side, just until the outside starts to brown and set. This step adds flavor and helps keep the filling in place.
Transfer the seared chicken to the prepared baking dish. Brush the tops with melted butter and, if you like, sprinkle a little extra shredded cheddar on top for a cheesy crust.
Bake in the preheated oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the cheese is bubbly.
If you want a crisper top, switch the oven to broil for the last 2-3 minutes, watching carefully so it doesn’t burn.
Let the chicken rest for 5 minutes before serving. This helps the juices redistribute and makes slicing easier.