Preheat the oven to 400ºF. Remove the broccoli from the freezer and let it thaw while the potatoes bake. Once thawed, roughly chop the broccoli into small pieces and set it aside until ready to use.

Wash the potatoes thoroughly, then dry them with a paper towel or a clean dish towel. Use a fork to prick several holes in the skin of each potato. Pour the olive oil into a small dish and use your hands to coat each potato in oil. Place the oiled potatoes on a baking sheet and season them with a pinch of salt. Bake the potatoes for about 60 minutes, or until they are tender throughout.

With about 15 minutes left in the baking time for the potatoes, start preparing the cheese sauce. Add the butter and flour to a medium-sized saucepan. Place the pot over medium heat and whisk the butter and flour together as they melt. Allow the mixture to bubble and foam, whisking continuously. Cook for an additional 2 minutes to remove the raw flour taste, but be careful not to let the flour brown.

Whisk the milk into the butter and flour mixture. Bring it to a simmer, whisking frequently. Once the mixture reaches a simmer, it will begin to thicken. When thick enough to coat the back of a spoon, remove the pot from the heat. Season the sauce with salt and garlic powder.

Gradually whisk the shredded cheddar into the sauce, adding it one handful at a time. Make sure each handful of cheese is fully melted before adding the next. Once all the cheddar has been incorporated, stir in the chopped broccoli.

When the potatoes are finished baking, carefully slice them open. Use a fork to slightly mash the insides of the potatoes. When ready to serve, place each potato on a plate or in a bowl, then ladle the broccoli cheese sauce over the top. Serve warm.