How to Make It
Preheat oven to 425°F with rack in top third of oven. Cut the very top off the garlic heads (just enough to expose the cloves). Place each head of garlic on a square of aluminum foil, and drizzle with olive oil. Loosely but securely wrap foil around garlic heads, and place directly on upper oven rack, seam sides up. Bake in preheated oven until golden brown and very soft, about 1 hour. Remove from oven, and let cool.
Meanwhile, toss potatoes with 1 tablespoon oil, 1 teaspoon salt, and pepper in a large oven-safe skillet or baking dish.
After garlic has roasted 20 minutes, place potatoes on upper oven rack, and roast, shaking skillet occasionally, 15 minutes. Meanwhile, toss shallots and sage with 1/2 teaspoon salt and remaining 1 tablespoon olive oil.
After potatoes have roasted 15 minutes, add shallot mixture to potatoes, distributing evenly and shaking the pan to incorporate, and roast 15 minutes.
Squeeze garlic cloves into a small bowl. Add cream, and stir with a fork, mashing the garlic and combining well. Add 1/2 teaspoon salt and pepper to taste.
Remove pan from oven, and use a potato masher or sturdy mug to flatten each potato. Pour cream mixture over potatoes, sprinkle with Parmesan, and return to oven on lower rack. Roast 20 minutes. Transfer to top rack, increase heat to broil, and broil until top is deep golden brown, for 3 to 5 minutes. Serve immediately.