Place broccoli in a microwave safe bowl with a splash of water, cover and microwave on high for 3 minutes. Set aside.

In a large skillet over medium high heat, melt the butter then add the flour and whisk for 1 minute until foamy and thoroughly combined. Whisk in the milk and turn up the heat. Continue whisking until milk simmers and begins to thicken. When milk is simmering, turn down the heat and let milk continue to cook for 2 minutes. Remove from heat and add cheese a bit at a time mixing until all cheese is added and melted. Stir in salt and chili powder then mix in the broccoli florets. Combine and set aside.

Preheat broiler and cut baked potatoes in half lengthwise.

Using a spoon, make shallow trough in cut side of potato to hold filling, leaving at least a ¼" border around edges. Be careful not to take too much potato out, just enough to keep filling from sliding off. Brush potatoes with butter, season lightly with salt and pepper. Turn potatoes over and butter and season the skin side. Place them on a baking sheet, skin side up and broil 2-3 minutes until starting to brown. Turn over and broil 2- 3 minutes more then remove from oven.

Sprinkle broccoli and cheddar cheese mixture evenly among the potato skins. Top with remaining cheese.

Broil about 3-4 minutes more until cheese is melted then remove from oven. Enjoy while still warm.