01 - Preheat oven to 400°F. Slice the tops from the garlic heads to expose the cloves. Remove any loose outer skins.
02 - Place garlic heads cut-side up on a piece of foil. Drizzle with 1 tablespoon olive oil and wrap tightly. Roast for 45 minutes, or until the garlic is golden and tender. Allow to cool, then squeeze the roasted cloves from the skins into a small bowl.
03 - Combine 3 tablespoons olive oil with the roasted garlic cloves in the bowl. Gently mash together to create a flavorful garlic oil for serving.
04 - Place peeled and quartered potatoes in a large pot and cover with cold water by 1 to 2 inches. Bring to a boil, then cook for 15 to 20 minutes, until potatoes are fork-tender. Avoid overcooking to prevent waterlogged potatoes.
05 - Drain potatoes thoroughly. Return to a bowl and mash until smooth using a potato masher or ricer.
06 - Heat heavy cream in the empty pot. Add hot mashed potatoes, Parmesan cheese, butter, and salt. Stir continuously over low-to-medium heat for approximately 5 minutes, until texture is creamy and ingredients are fully incorporated.
07 - Taste and adjust seasoning with additional salt if needed. Adjust the texture with more warm cream if desired.
08 - Transfer creamy mashed potatoes to a serving dish. Swirl in the reserved garlic-infused olive oil or more melted butter. Top with any remaining roasted garlic cloves, fresh thyme leaves, and freshly ground black pepper. Serve immediately.