Crust:
Using a food processor, pulse together the flour, sugar, and salt.
Add cold butter in chunks and pulse 5 to 8 times until butter is in small pieces.
Gradually add cold water and pulse until the dough starts to come together.
Transfer the dough to two pieces of plastic wrap, pat into discs, and refrigerate for at least 1 hour (it will be sticky).
On a lightly floured surface, roll out one portion of dough to about 1/8 inch thick. Cut 15 circles with a 4-inch round cutter.
Grease a muffin pan (12 cups) plus 3 additional muffin cups in another pan. Press each dough circle into the muffin cups. Refrigerate the prepared crusts while making the filling.
Filling:
Preheat the oven to 350°F (175°C).
Cream butter and brown sugar together until smooth.
Add eggs one at a time, then mix in the maple syrup, salt, and vanilla extract until combined.
Pour the filling into the prepared crusts, filling each about 2/3 full.
Bake for 25 minutes or until the filling is set but still slightly soft.
Allow the tarts to cool for 5 minutes in the pan before transferring them to a cooling rack.