Place potatoes and garlic in a large Dutch Oven and add water just to cover. Cover with lid and bring to a boil over medium-high heat. Season generously with salt (about 1 Tbsp.), lower heat to medium, and cook potatoes, uncovered, until very tender when pierced with a paring knife (but not falling apart), about 20 minutes. Save a little of the cooking water, then drain potatoes in a colander and shake to remove excess moisture.

Meanwhile, add cream and thyme to a medium Stainless Clad Saucepan and heat over medium-low until barely simmering. Remove from heat and set aside.

Place Dutch oven over medium-low heat. Using a potato ricer or food mill, immediately press hot potatoes and garlic back into Dutch oven, pausing to stir in butter a few tablespoons at a time. Continue until all the potatoes are pressed and all the butter is incorporated.

Discard thyme from warm cream mixture and use a wooden spoon or silicone spatula to gradually stir into hot potatoes. Continue stirring potato mixture until thickened, about 3 minutes.

Add the grated cheese by the handful, stirring vigorously to incorporate and waiting until each batch of cheese is fully melted before adding more. Continue stirring potatoes–you are looking for a very thick and stretchy consistency. Unlike standard mashed potatoes, you want to work these potatoes quite a bit to activate the starch. If necessary, add a few tablespoons of the reserved cooking water at a time to help melt cheese and achieve a smooth consistency.

Top with chives and serve hot.