Prepare the strawberry filling. Combine the chopped strawberries, granulated sugar, and cornstarch in a small saucepan. Cook over medium heat, stirring often, until the mixture thickens, about 5 to 7 minutes. Remove from heat and let it cool completely.
Unroll the thawed puff pastry sheets onto a lightly floured surface. If the sheets are rectangular, gently roll them slightly thinner to create a larger surface area.
Spread the cooled strawberry filling evenly over the surface of each pastry sheet, leaving a small border along one long edge.
Starting from the long edge opposite the border, tightly roll the pastry into a log. Pinch the seam closed to secure the roll.
Wrap each log tightly in plastic wrap and chill in the refrigerator for at least 30 minutes. This helps the pastry hold its shape during slicing.
Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper. Slice each chilled log into 8 equal rounds, about 1 inch thick.
Place the pastry swirls cut-side up on the prepared baking sheet, leaving space between them. Bake for 18 to 20 minutes, or until the pastry is golden brown and puffed.
While the swirls cool slightly, prepare the glaze. Whisk together the powdered sugar and milk until smooth. Add more milk if the glaze is too thick.
Drizzle the glaze over the warm pastry swirls. Serve warm or at room temperature.