1. Preheat oven to 350 degrees.

2. Pour cream into a large bowl; season with 1 teaspoon salt and 1/2 teaspoon pepper. Peel potatoes. Trim all sides of one potato to make a rectangular shape. Set a mandoline over bowl of cream and, starting with the flat side of the potato, slice potato lengthwise into very thin slices (alternatively, if you cannot set your mandoline over bowl, slice potatoes, adding slices to cream as you work). Toss potato slices in cream occasionally to keep them from oxidizing. Repeat process with remaining potatoes.

3. Brush a 10-by-5-by-2 3/4-inch-high baking pan with half of the softened butter. Line pan with parchment paper, leaving a 5-inch overhang on all sides. Brush parchment paper with remaining softened butter and sprinkle with salt and pepper.

4. Trim slices to form an even layer in the bottom of the pan; repeat process to form 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. Fold sides of parchment paper over potatoes. Cover pan tightly with aluminum foil and transfer to oven.

5. Bake until potatoes are completely tender when pierced with the tip of a sharp knife, about 1 hour and 50 minutes. Remove from oven and let cool for 15 minutes. Cut a piece of cardboard slightly smaller than the size of pan; wrap with aluminum foil. Place foil-wrapped cardboard on top of potatoes and weight down with heavy cans; let potatoes cool to room temperature. Remove weights and tightly wrap pan. Refrigerate potatoes at least 6 hours or up to 2 days.

6. To serve, run an offset spatula between the parchment paper and pan to release. Using the parchment paper overhang, carefully lift pave out of pan or invert onto a cutting board. Trim sides of pave and cut into 12 equal pieces; let stand at room temperature for 30 minutes.

7. Heat a large skillet over medium-high heat; add enough canola oil to coat. When oil is hot, add potatoes, cut-side-down, along with thyme and garlic. Cook, basting with oil, until browned on first side. Carefully turn and brown on opposite side.

8. Transfer potatoes to a serving platter and arrange browned side up. Place a small piece of butter on each and sprinkle with chives. Serve.