Preheat oven to 400F
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 no resistance), 45-50 minutes
If using Yukon Golds, placed on a rimmed baking sheet or in a large baking dish and cover tightly with foil. Roast until very tender, 80-95 minutes
Remove 4 cloves garlic from the head and set aside for the topping. Cut remaining head of garlic in half crosswise and place in a medium saucepan with 5 sprigs thyme, peppercorns, 1.25 cups (2.5 sticks) butter, 4 cups whole milk, and 1 tbsp kosher salt
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
When potatoes are done, use a paring knife to remove the skins - it's important to do this while they're very hot. After skins are removed, pass them through a potato ricer or food mill fitted with a fine disk into a large pot (or simply mash them in the pot with a potato masher)
Return garlic mixture to a simmer, then pour through a fine-mesh sieve into the pot with the potatoes. Discard the 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
Pulse reserved 4 cloves garlic in food processor until finely chopped, 15 seconds or so. Add bread and potato chips and process in long pulses until coarse crumbs form, about 1 minute
Heat remaining 4 tbsp 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 400F oven and bake, tossing every 5 minutes, until crumbs and chips are evenly dark golden brown, 15-20 minutes
Meanwhile, finely grate remaining lemon zest from reserved lemon into a small bowl. Add leaves from 3 sprigs thyme and paprika and toss to combine
Remove crumb mixture from oven and immediately toss in the thyme mixture. Taste and season with more salt if needed. Let topping cool in the pan, then add the parsley
To serve, transfer mashed potatoes to a large bowl and sprinkle topping over (or let people serve themselves potatoes and top with the topping separately)