1. Cook potatoes:
OVEN: Preheat oven to 400°. Pierce potatoes with a fork, and wrap each in foil. Bake until tender, 1 hour.
MICROWAVE: Pierce potatoes with a fork, and wrap each in a paper towel. Place in microwave, and cook on high 8 minutes, until just tender when pierced with a fork (potatoes will continue to cook when removed from microwave).
While potatoes are cooking, make sauce:
2. Combine milk and flour in a small saucepan, bring to simmer, and cook, whisking, until thickened, 2–3 minutes. Add cheese, salt, pepper, and cayenne, and whisk until sauce is smooth. Continue to simmer, whisking, an additional 2 minutes.
3. Heat broccoli in a heat-safe dish in the microwave for 4-5 minutes, until hot.
4. Split cooked potatoes open with a knife. Spoon 1/2 cup broccoli into each potato, and top with 1/4 cup Cheddar sauce.