Pour olive oil into a 9- to 10-inch square pan. Cut garlic heads in half crosswise through cloves and lay cut sides down in pan.
Bake in a 375° oven until garlic is golden brown on the bottom and oozing sticky juices, about 35 minutes. Slip a thin spatula under garlic to release from pan. Reserve 1 half-head of garlic; pluck or squeeze cloves from remaining garlic.
Meanwhile, rinse and peel potatoes. Cut into 2-inch chunks. Set on a rack over 1 inch boiling water in a 14-inch wok or a 5- to 6-quart pan. Cover pan and steam over high heat until potatoes mash very easily when pressed, 20 to 25 minutes.
Transfer potatoes to a large bowl. Add loose garlic cloves and cheese. With a potato masher or mixer, mash potatoes, adding enough broth to make them as soft and creamy as you like. (If you plan to serve potatoes as soon as they are mashed, heat broth before adding.) Season to taste with salt and swirl into a shallow 2 1/2- to 3-quart casserole.
Serve with a garnish of reserved roasted garlic. Sprinkle with pepper.