Preheat the oven to 400°F and line a baking sheet with parchment paper.

Add the mixed berries and granulated sugar to a small saucepan over medium heat. Cook for 3 to 4 minutes, stirring occasionally, until the berries soften and release their juices.

In a small bowl, stir together the cornstarch and 1 tablespoon water. Add the slurry and lemon juice to the saucepan and cook for 1 to 2 minutes more, stirring, until the filling thickens to a jammy consistency. Remove from the heat and cool for at least 10 minutes.

Lightly flour the work surface and roll the puff pastry slightly to smooth it into a neat rectangle. Cut it lengthwise into 8 even strips.

Spoon a narrow line of cooled berry filling down the center of each strip, leaving a small border at the ends.

Fold each strip lengthwise over the filling and gently press the edges to seal. Twist each strip a few times and place on the prepared baking sheet, spacing them apart.

Whisk the egg with 1 tablespoon water and brush the twists all over with the egg wash.

Bake for 18 to 22 minutes, until puffed and deeply golden brown.

Transfer the twists to a wire rack and cool for about 10 minutes.

Whisk together the powdered sugar, milk, and vanilla extract until smooth and drizzleable, adding a little more milk if needed. Drizzle over the warm twists and let set briefly before serving.