Using a food processor, pulse flour, sugar, and salt. Add cold butter in chunks, pulse 5 to 8 times, or until butter is in small pieces. Add cold water and pulse until the dough starts coming together.
Place dough on a flat surface and bring it together with your hands (pressing, not kneading). Divide the dough in 2 portions and cover with plastic film and refrigerate for at least 1 hour.
Sprinkle flour on a flat surface and roll out one portion at the time, about 1/8 of an inch thick. Use a round cutter or lid (4 inches) and cut 15 pieces.
Greasy 1 muffin pan completely and 3 muffin cups from a second pan. Press each dough circle into the bottom of a muffin pan cup. Refrigerate while making the filling.
Preheat the oven to 350F.
Cream butter and sugar. Add eggs one at the time. Add maple syrup, salt, and vanilla extract. Pour filling into pie crust and bake for 25 minutes.
Let the tarts cool for 5 minutes in the pan and remove to a cooling rack.