A buttery tart shell filled with thin apple slices arranged in a spiral, baked until the edges caramelize, and finished with homemade salted caramel and flaky sea salt.
Whisk 1 1/4 cups all-purpose flour, 1 tablespoon granulated sugar, and 1/2 teaspoon salt together in a large bowl.
Cut in 1/2 cup unsalted butter, cold and cubed until the mixture looks sandy with a few visible pieces of butter scattered through it.
Drizzle in 3 to 4 tablespoons ice water one tablespoon at a time, mixing gently, just until the dough holds together.
Shape it into a disk, wrap it tightly, and refrigerate at least 1 hour.
Preheat the oven to 375 degrees F.
Dust the work surface and roll the dough into a 12-inch circle.
Transfer it to a 9-inch tart pan with a removable bottom and press it gently into the bottom and sides without stretching.
Trim the excess at the rim. Return the shell to the refrigerator for 20 minutes.
Apple Filling
Slice the apples about 1/16 inch thick on a mandoline or with a very sharp knife.
Drop the slices into a bowl of cold water mixed with 2 tablespoons fresh lemon juice as you work. Drain well and pat completely dry with paper towels.
Whisk 1/4 cup light brown sugar, 2 tablespoons granulated sugar, 1 teaspoon ground cinnamon, 1/4 teaspoon ground nutmeg, 1 teaspoon vanilla extract, and 1 tablespoon cornstarch together in a large bowl.
Add the apple slices and toss gently until every slice is coated.
If using apple butter, spread 1/4 cup apple butter, optional in an even layer across the bottom of the chilled shell.
Beginning at the outside edge, overlap the apple slices tightly and stand them slightly upright, working inward in concentric circles until you reach the center.
Curl a few of the prettiest slices into a small rose and tuck it into the middle. Brush the tops lightly with 2 tablespoons melted butter.
Bake 45 to 55 minutes, until the crust is deeply golden and the apples are tender with caramelized edges. If the crust browns too fast, tent the edges loosely with foil for the last 10 to 15 minutes. Cool the tart in the pan about 20 minutes, then lift away the ring.
Caramel Sauce
While the tart cools, warm 1 cup granulated sugar in a heavy-bottomed saucepan over medium heat, stirring occasionally, until it melts to a smooth amber.
Whisk in 6 tablespoons unsalted butter until fully incorporated.
Pour in 1/2 cup heavy cream slowly, whisking constantly, until smooth.
Stir in 1 teaspoon vanilla extract and 3/4 teaspoon flaky sea salt. Let the caramel cool until thickened but still pourable.
Drizzle the caramel generously over the tart just before serving and finish with a light sprinkle of flaky sea salt and thyme leaves, if using. Slice and serve slightly warm or at room temperature.
Notes
Make the dough up to two days ahead and the salted caramel up to a week ahead.
Bake the tart the day before and drizzle the caramel just before serving.
Store covered in the refrigerator up to four days.