How to Make It
Preheat oven to 350°F. Drizzle garlic cloves with oil, and wrap garlic head in aluminum foil. Bake in preheated oven until cloves are very tender, about 45 minutes. Set aside.
Lightly grease a 9- x 5-inch loaf pan with olive oil and line with parchment paper, allowing 2 inches of overhang on both long sides. Place kosher salt and 5 roasted garlic cloves in a large bowl; using the back of a spoon, smash into a paste. Whisk in cream, thyme, and pepper. Set aside.
Using a mandoline, thinly slice potatoes lengthwise into 1/16-inch-thick slices. Add sweet potatoes to cream mixture; toss gently to coat. Layer potato slices in bottom of prepared pan, slightly overlapping to create a shingled layer, trimming potato slices if needed. Continue layering, pressing occasionally, until potatoes are about 1/2 inch from top of pan. Discard remaining cream and potatoes.
Fold excess parchment over potatoes, and cover pan with aluminum foil. Bake at 350°F until potatoes are tender, about 2 hours. Remove foil from pan, leaving parchment in place. Let cool 2 hours at room temperature. Place a second 9- x 5-inch loaf pan on top of cooled pavé in pan, and weigh it down with unopened canned goods. Refrigerate 8 hours or overnight.
Carefully remove top pan and weights. Pour off any accumulated liquid around pavé. Invert pavé onto a cutting board; remove and discard parchment paper. Cut pavé crosswise into 8 slices. Place slices on a rimmed baking sheet, and refrigerate 20 minutes or up to 4 hours.
Preheat oven to 500°F with rack in upper third of oven. Brush pavé slices generously with melted butter, and arrange in a single layer on baking sheet. Bake until bottom edges are browned, 6 to 10 minutes. Invert pavé onto a serving platter, and sprinkle with flaky sea salt. Serve hot.