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Step 1
Preheat oven to 450°F.
Step 2
Prick the sweet potatoes with a fork. Place them in the oven and roast for 45 to 50 minutes, until tender, or slightly longer depending on the size of the potatoes.
Step 3
Meanwhile, cut the broccoli into florets. Mince the garlic. In a large skillet, heat the olive oil, then add the garlic. Wait until the garlic sizzles, after about 30 seconds add the red pepper flakes, the broccoli, and a few pinches of kosher salt. Sauté the broccoli until bright green and tender, 5 to 7 minutes.
Step 4
Drain and rinse the beans. In the bowl of a food processor, blend the beans, ¾ cup water, ½ cup shredded cheese, and the kosher salt. Taste, and add additional seasonings if necessary, or additional water to make the sauce more creamy. Add the broccoli to the cheese mixture.
Step 5
After the sweet potatoes are baked, cut out the centers and remove some sweet potato (which can be saved and eaten later). Place the cheese and broccoli mixture into the hole in each potato, then top with additional shredded cheese. Place the potatoes back in the oven for a few minutes until the cheese is melted. Serve warm.