Ricotta, goat cheese, and fontina partner well with beets; their creaminess carries the roots' subtle candied-but-mineral flavor.
Preheat oven to 375 degrees. On a lightly floured surface, roll out dough 1/8 inch thick. Press firmly into a 13-by-9-inch rimmed baking sheet, leaving a 1-inch overhang on all sides. Tuck overhang under to create a double thickness; press firmly against pan. Pierce bottom of shell all over with a fork. Refrigerate or freeze until firm, about 30 minutes.
Line shell with parchment; fill with pie weights or dried beans. Bake until golden brown, about 30 minutes. Remove weights and parchment. Transfer to a wire rack to cool completely. (Keep oven on.)
Trim all but 1/2 inch of stems from beets; rinse well. Toss with oil and 1 teaspoon salt. Transfer to a rimmed baking sheet; cover with parchment, then tightly with foil. Roast until beets are tender, 45 minutes to 1 hour. When cool enough to handle, peel beets with a paring knife. Cut into thin rounds. Raise heat to 425 degrees.
Stir together goat cheese, ricotta, and chopped thyme until well combined; season with pepper. Spread mixture over tart shell, filling all the way to edges.
Arrange beets over cheese mixture, overlapping slices slightly and alternating colors, if possible. Lightly season with salt. Sprinkle fontina and whole thyme leaves on top. Lightly drizzle with oil, and season with pepper. Bake until golden brown, about 25 minutes. Serve warm.