Preheat the oven to 400 degrees . In a small saucepan, bring the cream, sage sprigs and garlic just to a boil over medium heat. Remove from heat; let steep.
Meanwhile, in a large bowl, toss the potatoes and squash with 1 1/2 cups cheese, 2 tsp. salt and 1 tsp. pepper. Transfer to a greased 3-qt. baking dish. Remove the sage and garlic from the cream mixture, then pour over the vegetables. Sprinkle with 1/2 cup cheese and more pepper.
Bake, covered, until the edges begin to bubble, about 30 minutes. Uncover, sprinkle with the remaining 1/4 cup cheese and bake until the vegetables are tender and the top is browned, 25 to 30 minutes. Let rest for 15 minutes before serving.