Thaw frozen puff pastry in the refrigerator overnight, or if you're in a hurry - on the counter for about 30 minutes, uncovered.Preheat oven to 400°F/200°C. Make egg wash by whisking egg with 1 tablespoon of water, then set aside. Combine room temperature cream cheese with lime zest, a teaspoon of lime juice, and ¼ cup powdered sugar in a small mixing bowl. Whisk to thoroughly combine until it is smooth and uniform. Set aside.
In a medium bowl, toss blackberries with vanilla bean paste (or vanilla extract) and remaining lime juice, then set aside.
Remove puff pastry from fridge. It will be folded in thirds. Gently open it up, like a brochure, on a clean kitchen towel or lightly floured surface. Using a rolling pin, lightly roll over the dough, just to even it out and level the creases a bit - do not use much pressure, we don't want to make it thinner.
Using a sharp Chefs knife or a pizza cutter, cut the sheet of dough into 6 equal pieces. Place them on a parchment-lined baking sheet. Then score a border along the edges with a paring knife. Use a fork to dock the middle of the puff pastry.
Spread about 2 tablespoons of the cream cheese mixture in the middle of each piece of puff pastry. (I use an offset spatula for this.)
Pile the blackberries on top of the cream cheese mixture and lightly press them down to secure in place. Brush edges of puff pastry with egg wash.
Bake for 16 – 18 minutes, or until puffed and golden. Let them cool on the sheet pan.
While the tarts are cooling, whisk together the powdered sugar and milk for the glaze. When tarts have cooled completely, drizzle glaze over the tarts, and add additional lime zest, if desired.Store leftover tarts in an airtight container in the fridge for up to 3 days.