Step 1

Preheat oven to 400°. If using German Butterballs, place potatoes on a rimmed baking sheet or in a cast-iron skillet and roast, turning halfway through, until very tender (a paring knife inserted into the center should meet with no resistance), 45–50 minutes.

Step 2

If using Yukon Golds, place on a rimmed baking sheet or in a large baking dish and cover tightly with foil. Roast until very tender, 80–95 minutes.

Step 3

Meanwhile, remove 4 garlic cloves from garlic head and set aside for the topping. Cut remaining head of garlicin half crosswise and place in a medium saucepan with thyme, peppercorns, butter, 4 cups milk, and 1 Tbsp. salt.

Step 4

Using a vegetable peeler, remove wide strips of zest from half of lemon and add to pot; set lemon aside for the topping. Bring mixture to a simmer over medium-high heat, stirring occasionally. Immediately remove from heat, cover, and let sit at least 30 minutes.

Step 5

When potatoes are done, use a paring knife to remove skins (it’s important to do this while they are very hot; hold them in a kitchen towel to protect your hands), then pass them through a ricer or food mill fitted with the fine disk into a large pot (or simply mash them in the pot with a potato masher).

Step 6

Return garlic mixture to a simmer, then pour through a fine-mesh sieve into pot with potatoes; discard solids. Set potato mixture over medium heat and whisk until liquid is incorporated and potatoes are very smooth and bubbling. Taste and season with more salt if needed. Cover and keep warm until ready to serve.

Step 7

Do Ahead: Potatoes can be made 2 days ahead. Transfer to an airtight container and let cool. Cover and chill. Reheat over medium, whisking constantly and loosening with more milk if needed.

Step 8

Pulse reserved 4 garlic cloves in a food processor until finely chopped, about 15 seconds. Add bread and potato chips and process in long pulses until coarse crumbs form, about 1 minute.

Step 9

Heat butter in a large ovenproof skillet over medium until foaming. Add breadcrumb mixture and season with salt and pepper. Cook, stirring, until mixture is coated in butter and fragrant, about 1 minute. Transfer skillet to oven; bake, tossing every 5 minutes, until crumbs and chips are evenly dark golden brown, 15–20 minutes.

Step 10

Meanwhile, finely grate remaining lemon zest from reserved lemon into a small bowl. Add thyme leaves and paprika and toss to combine.

Step 11

Remove crumb mixture from oven and immediately toss in thyme mixture. Taste and season with more salt if needed. Let topping cool in pan, then add parsley.

Step 12

To serve, transfer mashed potatoes to a large bowl and sprinkle topping over.

Step 13

Do Ahead: Topping (without parsley) can be made 2 days ahead. Store airtight at room temperature.