Preheat oven to 400 degrees Fahrenheit. Take out a rimmed baking sheet and set aside.
Line work surface with parchment paper and roll out puff pastry dough on it. Cut into 6 pieces by cutting in half lengthwise and in thirds crosswise. (There's no need to separate them, as they'll bake up separately.)
With a fork, dock the pastry to within 1/2" of the edges of the pieces. The easiest way to is perforate the dough in a rectangle first, like you're using each rectangle of dough as a guide to make a smaller rectangle inside of it, then poke the middle 5 or 6 times all over. (This helps keep the middle sunken while the edges puff up.)
In a small bowl or liquid measuring cup, whisk the egg and water until well blended; brush on the edges of the pastry pieces.
In a large mixing bowl, beat the cream cheese, sugar, lemon juice, and vanilla extract until smooth. Spread over the inner rectangles on each pastry piece, dividing evenly among them. Be careful not to go all the way to the edges!
In a small bowl, mix together the preserves and basil until well blended. Drop large spoonfuls into the centers of the pastry rectangles, dividing evenly.
If desired, sprinkle sanding sugar on the edges of the pastries.
Slide the parchment paper with the pastry onto the rimmed baking sheet. Bake for 17-19 minutes, or until golden.
Cool on baking sheet for 5 minutes before transferring to cooling rack to cool completely.