Make the Dough: Cream together the sugar and margarine on medium speed until light and fluffy. Reduce the mixer speed to low and add the salt, eggs, flour and milk. Continue to mix until just about all of the flour is incorporated. Add the baking powder, baking soda and vanilla extract and mix to combine. The dough will be very soft and sticky. Cover with plastic wrap and refrigerate for at least 30 minutes to 1 hour.
Make the Filling: In a small saucepan, whisk together the sugar, cornstarch and ¼ cup of the water to form a paste. Stir in the remaining water, lemon juice and raisins. Set the pan over medium heat and cook, stirring frequently, until the mixture thickens and the raisins plump, about 5 to 10 minutes. Cool to room temperature before using.
Assemble and Bake the Cookies: Preheat oven to 400 degrees F. Line three baking sheets with parchment paper or a silicone baking mat.
Using about 1/3 of the dough at a time, roll out the dough on a well-floured surface to about 1/8-inch thickness. (The dough is very soft and sticky, so use as much flour as necessary to roll it out without it sticking.) Cut the dough into rounds (I used a 2¾-inch cookie cutter). Place one on prepared baking sheet, spoon 1 to 2 tablespoons of the raisin filling onto the circle and then top with another round of dough. Just lay the circle on top of the filling; there is no need to seal them shut, as they will do so while baking. Repeat with remaining dough and filling.
Bake the cookies until lightly golden brown on top, about 15 minutes. Allow to cool for about 10 minutes on the pan and then transfer to a cooling rack to cool completely. Store in an airtight container at room temperature for up to 5 days.