Heat oven to 375° F. In a small saucepan, combine the milk, cream, garlic, and thyme. Bring to a boil. Remove from heat; set aside for 10 minutes. Discard the garlic and thyme.
Meanwhile, coat a 2-quart gratin dish or ovenproof casserole with vegetable cooking spray. Cut the fennel lengthwise into 1/4-inch slices. Cut the potatoes crosswise into 1/4-inch thick slices.
Place a layer of potatoes in the dish and season with salt and freshly ground pepper. Overlap with a layer of fennel and half the cheese. Repeat with the remaining potatoes, fennel, and cheese. Pour the infused milk over the vegetables.
Bake until the gratin is golden and the vegetables feel tender when pierced with a fork, 40 to 50 minutes. Remove from oven 15 minutes before serving.