Preheat the oven to 375°F. Wash and trim the asparagus spears. Peel and thinly slice potatoes. In a large bowl, whisk together heavy cream, minced garlic, salt, and pepper. Arrange a layer of sliced potatoes in a baking dish. Top with a layer of blanched asparagus spears. Pour some of the cream mixture over the vegetables. Repeat the layers until all the vegetables and cream mixture are used up. Cover with foil and bake for 45-50 minutes, until the potatoes are tender. Remove the foil and bake for another 10-15 minutes, until the top is golden brown and bubbly. Let cool for 10 minutes before serving.