Step 1

Preheat the oven to 425 degrees Fahrenheit (218 degrees Celsius). Line a baking sheet with foil or a baking mat, and set it aside.

Step 2

Place scrubbed, dried potatoes on the baking sheet. Rub each with oil, sprinkle with sea salt, and prick with a fork three times on each top. Bake for 1 hour or until fork-tender (this could take up to 1 hour and 15 minutes). Remove from the oven and allow to cool.

Step 3

Meanwhile, in a small saucepan set over medium heat, add the butter. When the butter has melted, whisk in the flour, and cook for 1 minute. Slowly add milk, whisking to create a smooth sauce. Bring the mixture to a low simmer.

Step 4

Add salt, pepper, garlic powder, onion powder, and paprika. Simmer until thickened, about 5 minutes. Remove from heat and stir in cheese, then broccoli.

Step 5

Remove the top of the potatoes, then score the inside and remove about 2 tablespoons of potatoes (you can spoon it onto the tops and serve it with it). Scoop a generous amount of the sauce inside of each potato. Return the reserved potato and top back. Serve immediately.