Preheat oven to 350°. Rub bottom and sides of a 5- by 9-inch loaf pan with 1 tablespoon butter. Line pan with parchment paper, leaving a 5-inch overhang on all sides. Rub parchment paper with 1 tablespoon butter and sprinkle with salt and pepper. Cut remaining 3 tablespoons butter into ¼-inch cubes.

Pour cream into a large bowl; season with 1 teaspoon salt and ½ teaspoon pepper. Trim potatoes to fit width of pan. Set a mandoline over bowl and slice potatoes lengthwise into thin slices. Toss slices in cream as you go.

To form pavé, place potato slices into prepared pan in an even layer; make a second layer. Dot with a few cubes of butter; season with salt and pepper. Continue layering potatoes and adding butter and seasoning after every two layers until pan is filled to the rim. Fold sides of parchment over potatoes. Cover pan tightly with aluminum foil, place it on a baking sheet, and slide it into the oven.

Bake until potatoes are tender when pierced with a skewer, about 90 minutes. Remove pavé from oven and cool for 15 minutes. Cut a piece of cardboard slightly smaller than the top of the pan, wrap with aluminum foil, place it on potatoes, and weigh it down with heavy cans until the pavé is room temperature. Refrigerate pavé 6–48 hours.

To serve, run a spatula between parchment paper and pan to release pavé. Lift pavé out of pan and place it on a cutting board. Cut into 6 slices, 1 ½ inches thick each.

Heat a large skillet over medium-high heat; add enough vegetable oil to coat bottom. When oil is hot, add thyme and garlic. Add potatoes (cut side down) and cook, basting with oil, until browned on first side. Turn and brown on opposite side. Transfer slices to a platter and sprinkle with chives before serving hot.