In a large bowl, beat the unsalted butter and granulated sugar together on medium-high speed for 1-2 minutes, until light and fluffy.
Add the large egg, lemon zest, and vanilla extract and mix until fully combined.
Scrape down the sides and mix again for 10-20 seconds.
Add the all-purpose flour and salt and mix until just barely combined in a crumbly dough.
Use your hands to press the dough together. If the dough is too dry, add water one tablespoon at a time to help it come together.
Form the dough into a disk and wrap it with plastic wrap. Chill for 2 hours.
While the dough is chilling prepare the poppy seed filling.
Once the dough is chilled, preheat the oven to 350°.
On a lightly floured surface, roll the dough out to 1/8 inch thick.
Use a 3-inch round cookie cutter to cut out rounds of dough.
Carefully transfer the rounds to parchment-lined baking sheets leaving 1 inch between them.
Place 1 teaspoon of poppy seed filling or jam in the center of the dough.
Fold up the side of the dough to form a triangle around the filling, pinching the corners together to prevent leaking while baking.
Bake for 12-15 minutes, or until the cookies are just starting to turn golden brown around the corners.
Let them cool on the baking sheet for 10 minutes before transferring to a cooling rack.