Step 1: Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper.
Step 2: On a lightly floured surface, carefully unfold the thawed puff pastry sheet. Using a sharp knife or pizza cutter, lightly score a border about 1/2 to 3/4 inch (1.5-2 cm) from the edges of the pastry. Do not cut all the way through.
Step 3: Prick the inner rectangle of the pastry all over with a fork. This prevents it from puffing up too much during baking.
Step 4: In a small bowl, combine the granulated sugar and all-purpose flour. Sprinkle this mixture evenly over the inner rectangle of the pricked puff pastry.
Step 5: Arrange the apricot halves, cut-side up, in neat rows or a decorative pattern within the scored border on the pastry. You can overlap them slightly.
Step 6: Carefully transfer the assembled tart to the prepared baking sheet.
Step 7: Bake for 20-25 minutes, or until the pastry is deeply golden brown and puffed around the edges, and the apricots are tender. Keep an eye on it; if the edges brown too quickly, you can loosely tent with foil.
Step 8: While the tart is still warm, gently heat the apricot jam in a small saucepan over low heat until it's melted and runny. If it's too thick, you can add a teaspoon of water to thin it slightly.
Step 9: Using a pastry brush, generously brush the warm, melted apricot jam over the baked apricots and the puffed pastry edges. This creates a beautiful, glossy glaze.
Step 10: Let the Puff Pastry Apricot Glazed Tart cool completely on a wire rack before slicing and serving. Optionally, dust with powdered sugar just before serving.