Here's the cure for the winter doldrums: a showstopping savory tart in bright shades of orange and magenta, with sweet root vegetables accented by fennel, onion, thyme, and goat cheese. Serve warm or at room temperature–perfect for entertaining.
Preheat oven to 475° and set rack to bottom position. Line a baking sheet with foil, shiny side up. Set aside.
Make the dough: In a medium-size bowl, whisk together flour and salt. Sprinkle butter over flour mixture and use your fingers to work it in (rub your thumb against your fingertips, smearing the butter as you do). Stop when the mixture looks like cornmeal, with plenty of lumps. Sprinkle 3 tablespoons ice water and stir with a fork until dough comes together. If needed, add an additional tablespoon ice water. Turn out onto a lightly floured surface and knead three times. Dough should look mottled, with streaks of butter. Gather into a ball; then press into a disk and wrap in plastic. Refrigerate at least 30 minutes (up to 3 days).
Meanwhile, make the filling: In a medium-size bowl, toss sweet-potato slices with 2 tablespoons oil and ¼ teaspoon salt. Spread slices out on one of the prepared baking sheets. In the same bowl, toss beet slices with remaining oil and salt. Spread out on the other baking sheet. Roast vegetables in oven until golden around edges, about 30 minutes.
Meanwhile, melt butter in a large skillet over medium to medium-high heat. Add fennel, onion, thyme, and sugar; cook until golden around the edges, about 15 minutes.
Prepare the crust: Lay an ovenproof silicone mat or large piece of parchment on your counter and sprinkle with flour. Turn dough in flour to coat. Working from center, roll dough out, lifting and turning it as you go to keep it from sticking, until you have a 13-inch circle.
Spread fennel/onion mixture in center of dough, leaving a 2- to 3-inch rim around the outside. When potatoes and beets are done, lower oven heat to 400°, and arrange them, overlapping, in concentric circles on top of onion mixture. Sprinkle with goat cheese. Fold edges of dough up and over filling to create a rim.
Transfer galette from silicone or parchment to foil-lined baking sheet and bake 10 minutes; then lower heat to 375° and bake until nicely browned around the edges, 20 to 30 minutes more. Sprinkle with fresh thyme leaves if you like, and serve warm or at room temperature.