Start by preheating your oven to 400°F so it's fully hot by the time your tarts are ready. Line a large baking sheet with parchment paper or a silicone mat. This keeps the bottoms from sticking and helps the crust bake evenly all the way through.
In a mixing bowl, beat the softened cream cheese with sugar, lemon zest, and vanilla extract until it's completely smooth. I like to scrape down the sides of the bowl once or twice so there are no lumps left. Set this aside while you work on the pastry.
Unroll your thawed puff pastry sheet and gently smooth it out with a rolling pin. You're not trying to stretch it thinner, just even out any creases from folding. Working on a lightly floured surface keeps the dough from sticking as you roll.
Using your larger cookie cutter, cut circles out of the pastry and space them a few inches apart on the baking sheet. Then press your smaller cutter into the center of each circle without cutting all the way through. This creates a border that puffs up around the filling.
Take a fork and gently poke the center of each pastry circle a few times. I usually make a small X pattern. This step keeps the middle from puffing up too much and losing its shape under the filling.
Spoon a small amount of the cream cheese mixture into the center of each circle, spreading it just up to the scored line. Then arrange your berries on top, pressing them lightly so they stay put once baked.
Whisk the egg with a tablespoon of water and brush it over the exposed pastry edges using your pastry brush. This gives the crust that shiny, golden-brown finish. Bake for about 15 minutes, until the edges are puffed and deeply golden.
Let the tarts rest on the baking sheet for five minutes before moving them to a wire rack. Once they've cooled slightly, dust them with confectioner's sugar for a soft, snowy finish that also looks great in photos.