Pre-heat the oven to 400. Line a baking sheet with parchment paper and set aside.
In a small dish, combine the salt, paprika, pepper, and garlic powder and stir together until mixed.
Place the chicken breasts on a cutting board. Using a sharp knife, slice the breasts from the side (creating a top and bottom) almost all the way through. Sprinkle the outside of each breast on both sides with the spice mixture from step two.
Place the broccoli florets in a microwave-safe bowl and cover the bowl with a damp paper towel. Microwave for 2 minutes on high. Remove from the microwave and stir in the softened cream cheese, shredded cheddar, and a sprinkle of salt and pepper until well combined.
Open each breast at the slit. Divide the broccoli/cheese mixture evenly amongst the four breasts and spread across the surface of one side (leaving the other half empty to fold over the filling). When all four breasts are topped on one side, fold the empty half over the filling to make a stuffed breast.
In a large skillet, add the oil and bring over medium-high heat. Working in batches of two at a time so as not to crowd the pan, add the stuffed chicken breasts to the pan and cook for about 1-2 minute(s) until the bottoms are seared golden. Flip the breasts and cook for another minute on the other side to do the same. Transfer the breasts to the prepared baking sheet.
Place in the pre-heated oven. Bake for 20-25 minutes until chicken is fully cooked through.