Heat oven to 400°F. Line a large baking sheet with parchment.
Dust the counter with flour. Roll puff pastry to a thin rectangle.
Move pastry to the sheet. Score a 1-inch border and dock the center.
Toss sliced apples with lemon juice, sugars, cinnamon, salt, cornstarch, and vanilla.
Arrange apples inside the border, slightly overlapping in rows.
Brush apples and pastry edges with melted butter. Sprinkle with coarse sugar.
Bake until apples are tender and pastry is deep golden, 30 to 35 minutes.
Warm apricot jam with a splash of water. Brush over hot apples to glaze.
Cool 10 minutes. Slice and serve warm or at room temperature.