Heat oven to 400°F. Line two baking sheets with parchment.
Combine berries, granulated sugar, cornstarch, lemon juice, and 3/4 tsp vanilla. Stir and let sit 5 minutes.
Unfold puff pastry on a lightly floured surface and roll each sheet just to smooth seams.
Spread a thin, even layer of the berry mixture over one sheet, leaving a 1/2-inch border. Top with the second sheet and press to seal.
Cut the stacked pastry into 12 strips (about 1 inch wide). Twist each strip several times and place on sheets.
Brush twists lightly with milk and sprinkle with coarse sugar.
Bake until puffed and deep golden, 16–18 minutes. Cool on the pan 5 minutes, then transfer to a rack.
Whisk powdered sugar, 1.5 tbsp milk, 1/4 tsp vanilla, and lemon zest until smooth. Drizzle over warm twists.