If using homemade pie dough: Line a large plate with parchment. Roll one portion of dough into a 10-inch round and transfer to prepared plate. Working around circumference, fold ½-inch of dough over itself and pinch to create a 9-inch round with a raised rim. Cut three 2-inch shallow slits in center of dough, and refrigerate for at least 2 hours and up to 24 hours. (If refrigerating overnight, cover dough with plastic wrap.) If using store-bought puff pastry: On a lightly floured surface, roll puff pastry large enough to cut out a 10-inch round. Place an inverted 10-inch skillet, bowl, or cake pan on the dough, then cut around it to form a circle. Transfer dough to a large parchment-lined plate. Working around circumference, fold ½-inch of dough over itself and pinch to create a 9-inch round with a raised rim. Using a fork, prick bottom of dough all over, and refrigerate for at least 2 hours and up to 24 hours. (If refrigerating overnight, cover dough with plastic wrap.)

Adjust oven rack to middle position. Preheat oven to 400°F (200°C). In a medium stainless steel skillet, melt 1 tablespoon (½ ounce; 14 g) butter over medium-high heat. Add onion and cook, stirring occasionally, adding 1 tablespoon of water at a time as needed to prevent scorching, until caramelized and deep golden brown, about 15 minutes. Stir in sherry, using a wooden spoon to scrape any browned bits from bottom of skillet. Add stock, bring to a simmer over medium-high heat and cook, stirring occasionally, until mixture is jammy and liquid has thickened, 6 to 10 minutes. Stir in thyme and ¼ teaspoon kosher salt. Remove from heat; set aside.

In a 10-inch oven-safe skillet, spread remaining 3 tablespoons (1 ½ ounces; 43 g) butter evenly over bottom. Sprinkle sugar, pepper, and remaining ¼ teaspoon kosher salt evenly over butter. Arrange tomatoes in an even layer over butter.

Transfer skillet to stove. Cook over high heat without stirring until tomatoes have slightly softened and butter-sugar mixture is amber, about 6 to 8 minutes, rotating skillet occasionally to maintain even browning. Remove from heat.

Spoon caramelized onions into empty spaces among tomatoes. Evenly top tomatoes with Gruyère.

Spread mustard evenly over prepared dough or pastry within rim, and carefully invert the dough over tomatoes, mustard-side down, making sure dough or pastry is centered.

Bake until crust is deep golden brown, 30 to 35 minutes. Transfer skillet to wire rack and let cool for 5 minutes.

Place a large plate over skillet, then carefully invert tart onto plate. Rearrange any tomatoes that have shifted during unmolding. Allow to cool slightly, about 20 minutes. Top with thyme, flaky sea salt, and additional pepper. Serve.