Look for fennel bulbs that are about 4 inches tall after trimming. Do not core the fennel bulb that is cut into wedges.

Adjust oven rack to middle position and heat oven to 375 degrees. Dust counter lightly with flour. Unfold puff pastry and roll into 11-inch square. Using pizza cutter or sharp knife, cut pastry into 11-inch circle. Transfer to parchment paper–lined rimmed baking sheet, cover loosely with plastic wrap, and refrigerate while preparing filling.

Swirl 2 tablespoons oil in bottom of 10-inch ovensafe nonstick skillet, then sprinkle with sugar and ¼ teaspoon salt. Arrange fennel wedges in pinwheel shape, fanning out from center of circle. Fill in gaps with sliced fennel. Cook, without stirring, over high heat until fennel turns deep golden brown, 7 to 9 minutes.

Off heat, sprinkle with apple, sage, and ¼ teaspoon salt. Carefully transfer chilled dough to skillet, centering over filling. Being careful of hot skillet, gently fold excess dough up against skillet wall (dough should be flush with skillet edge). Using paring knife, pierce dough evenly over surface 10 times. Transfer skillet to oven and bake until crust is deep golden brown, about 45 minutes. Transfer skillet to wire rack and let cool for 10 minutes.

Meanwhile, whisk vinegar, mustard, remaining 1 tablespoon oil, and remaining pinch salt together in large bowl. Add watercress and hazelnuts and toss to coat. Season with salt and pepper to taste.

Run paring knife around edge of crust to loosen. Using dish towels or potholders, carefully place serving platter on top of skillet, and, holding platter and skillet firmly together, invert tart onto serving platter. Transfer any fennel slices that stick to skillet to tart. Sprinkle with goat cheese, if using, and serve immediately with salad.

Assembling Fennel-Apple Tarte Tatin