Preheat oven to 425°F.
In a small bowl, whisk together paprika, onion powder, garlic powder, thyme, oregano, basil, cayenne, 1 teaspoon kosher salt and 1/2 teaspoon pepper. Pat fish dry and coat both sides with a teaspoon of blackening seasoning.
Lay out four 12-inch sheets of foil on a large baking sheet. Divide broccoli evenly among the four sheets and top with a tablespoon of butter; season with salt and pepper.
Top broccoli with a seasoned fish filet and spread another tablespoon of butter on top. Tightly fold up the edges of the foil to create a sealed packet. Transfer to a baking sheet. Bake for 12-15 minutes, or until the fish is cooked through. Carefully open the packets and transfer broccoli and fish to a plate. Serve with lemon wedges.