Prepare the potatoes. See note 3 for detailed instructions. Meanwhile, thaw the frozen broccoli, chop finely, and measure 2 cups.
Heat a medium pot over medium-low heat and melt the butter. Add flour, paprika, garlic powder, mustard powder, cayenne pepper, and salt. Whisk constantly for 1–2 minutes, until fragrant. Avoid browning or burning the mixture.
Very gradually pour in the milk, while whisking constantly. Increase heat to medium-high and whisk until the mixture boils and thickens, about 1 minute. (See note 4 for doneness.)
Off heat, add the shredded cheese a handful at a time, stirring until melted before adding more. Stir in the diced broccoli and adjust seasonings as needed.
Slice the baked potatoes in half and lightly mash the insides with a fork. Ladle the broccoli cheese sauce over the potatoes and serve immediately.
Video
Notes
Note 1: Use frozen broccoli for convenience. Thaw before chopping to make it easier to dice.Note 2: Shred sharp Cheddar cheese fresh off the block for better flavor. Avoid pre-shredded cheese, as it may not melt as smoothly.Note 3: Thoroughly clean potatoes and then follow the directions below to prepare your potatoes:
Air Fryer: Prick with a fork, and rub with oil and salt. Air fry at 400°F for 35–45 minutes, flipping halfway.
Microwave: Scrub potatoes, prick with a fork, and microwave on high for 5–10 minutes, flipping halfway.
Instant Pot: Place potatoes on a trivet, add 1 cup of water, and pressure cook on high for 12–20 minutes, depending on size.
Slow Cooker: Scrub potatoes, prick with a fork, and rub with oil and salt. Cook on high for 4–5 hours or low for 7–8 hours.
Note 4: The sauce should coat the back of a wooden spoon. Drag your fingertip across the back of the spoon; if it leaves a clear line, the sauce is ready.Nutrition Note: The nutrition information is calculated based on 6-ounce potatoes. Potato size varies greatly, so use this as a guide.Storage: Store the potatoes in an airtight container in the fridge and the sauce separately in another container. To reheat, warm the sauce on the stovetop, adding a splash of milk to thin if needed. Reheat the potatoes in the oven, air fryer, or microwave.