Place potato slices in a large pot; cover with water and 1 teaspoon salt. Bring to a boil over high heat and let boil until potatoes are just fork-tender. Drain and rinse to cool slightly.
Preheat oven to 350 F. Butter a 9x13-inch ovenproof baking dish and layer in potato slices. Blend cream with roasted garlic, rosemary leaves, 1/2 teaspoon salt, and pepper in a blender or food processor. Pour cream mixture over potatoes, then evenly sprinkle Asiago on top. Bake 15 to 20 minutes, until lightly browned and bubbling and potatoes are fully cooked through. Top with crispy garlic and serve.
*Roasted garlic can be made ahead of time. Trim the top of a bulb of garlic until cloves are visible, drizzle with olive oil, wrap in aluminum foil, and roast at 350 F for 45 to 60 minutes, until cloves are mushy soft and light to medium brown. Pull cloves out of husk with the tine of a fork and refrigerate until ready to use. (Leftovers will keep in fridge for 7 days, in freezer for 3 months.)
**To make crispy garlic, gather 8 large garlic cloves, ¼ cup olive oil, and salt for sprinkling. Set a strainer over a small, heat-safe bowl and set aside. Pour oil into a small skillet over medium heat. Test oil temperature by tossing a piece of garlic in — when bubbles immediately form around it, the oil is ready. Carefully slide garlic into the oil. Stir continually with a wooden spoon until pale golden brown, 3 to 5 minutes. Immediately transfer to the strainer, letting oil drain off the garlic. Spread garlic across paper towels to soak up remaining oil and sprinkle with ¼ teaspoon salt. When cool, transfer fried garlic to an airtight container and keep at room temperature. Reserve oil in fridge for future uses.
