In a food processor, pulse flour and salt together. Add cold butter cubes and pulse until the mixture resembles coarse crumbs. Add sugar, egg, and vanilla, then pulse just until the dough comes together. Don't overmix—you should still see small butter pieces for the flakiest crust!
Form the dough into a disk, wrap in plastic wrap, and refrigerate for at least 30 minutes.
Fill a large bowl halfway with cold water and add the lemon juice. Core the apples and slice them in half from top to bottom. Using a mandoline or very sharp knife, cut the apples into paper-thin slices (about 1/16 inch thick). Immediately place the slices in the lemon water to prevent browning.
Preheat your oven to 375°F (190°C). Roll out the chilled dough on a floured surface to about ¼-inch thickness. Transfer to a 9-inch tart pan with a removable bottom. Press the dough gently into the corners and trim any excess. Prick the bottom several times with a fork.
Line the tart shell with parchment paper and fill with pie weights or dried beans. Blind bake for 15 minutes, then remove the weights and parchment and bake for an additional 5 minutes until just barely golden. Let cool while preparing the apple roses.
Mix sugar, cinnamon, and nutmeg in a small bowl. Drain apple slices and pat them dry with paper towels. In a microwave-safe bowl, heat the apple slices for 45-60 seconds until slightly softened and pliable but not mushy.
Arrange 5-6 apple slices in a straight line, slightly overlapping, on a flat surface. The curved side (skin side) should be facing away from you. Brush with melted butter and sprinkle with the cinnamon-sugar mixture. Carefully roll up the apple slices from one end to the other, creating a rose shape. Transfer to a plate and repeat with remaining apple slices.
Arrange the apple roses in the par-baked tart shell, starting from the outside edge and working your way to the center. Fill any gaps with smaller apple roses or individual slices.
Brush the tops of the roses lightly with melted butter and sprinkle with any remaining cinnamon-sugar mixture. Cover the edges of the tart with aluminum foil to prevent over-browning.
Bake for 35-40 minutes until the apples are tender and the crust is golden brown. If the tops of the roses start to brown too quickly, loosely cover the tart with foil.
Allow the tart to cool for 10 minutes. Warm the apricot jam in the microwave for 20 seconds, then strain if chunky. Gently brush the warm jam over the apple roses for a beautiful shine that also helps preserve their color and moisture.
Let the tart cool completely before removing from the pan and slicing.