Defrost the pie dough according to the directions on the package. Preheat oven to 400°F with rack in center of oven. Line a large baking tray with parchment paper or Silpat liner.
In a large bowl, combine 8 ounces soft cream cheese, 1/4 cup sugar, 1 egg yolk, 1/2 teaspoon vanilla extract, and 1 teaspoon lemon peel. Beat mixture together on medium/high speed until creamy and smooth.
Open the first sheet of puff pastry on a clean work surface and gently roll it into a 10 x 10 square. Use a pizza cutter to cut each sheet into 12 equal slices.
Combine 2 of the strands by pinching the ends together tightly and then twisting the strand from top to bottom. Press one end to your work surface and wrap the twist tape around it, center outward. Pinch the end to secure it to the pastry. Flatten the center a little with fingertips and poke the center a few times with a fork to prevent the center from puffing out too much.
Place 1 tablespoon of the filling in the center and press the berries halfway into the cream. Repeat steps 2, 3 and 4 for the remaining strands and the second sheet of puff pastry. Transfer the filled pastry to a lined baking sheet, leaving at least 1/2 of a space between them.