Adapted from Serious Eats. I chose to follow their suggestion of using tapioca starch instead of the more traditional corn starch because that is what I had. I also used their method (which is also my mom's method) for making the dulce de leche.
Place racks at bottom and top thirds of the oven. Preheat oven to 350 F. Line 2 baking sheets with parchment paper. Set aside.
Add ground vanilla beans with flour, tapioca starch, powdered sugar, salt and baking powder to the bowl of a food processor. Process to mix thoroughly. Add the butter and pulse until you have a fine, sandy meal.
Divide dough in half. Create a clean workspace--I like to put down a silicone mat. Dust the surface generously with powdered sugar.
Place half of the dough in a ball onto the dusted surface and pat gently into a disc. Dust the top of the dough lightly with powdered sugar. Roll dough until you have a rough circle with about 6 inches in diameter. Dust with more powdered sugar, flip the 6 inch disc, and dust again.
Continue rolling until dough is between 14 and 1/8 inch (1/4 inch is more traditional but I found it easier to get closer to 1/8 inch. Either way be consistent). Slide a thin offset spatula under the edges of the dough circle to loosen any places that might have stuck. Use a 2 inch round cutter to cut circle cookies around the outside edges of the dough. Remove those cookies to the prepared baking sheets 1/2 inch apart (1 got 20-25 cookies to a sheet).
Slide the thin offset spatula under the new edges of the dough circle to again loosen any places that might have stuck. Repeat cutting out dough circles until you have only scraps. Gather the scraps, briefly knead, and reroll and cut as before. Repeat with remaining dough, until you have used all of the dough.
Bake about 9-15 minutes (depending on how thick your cookies are) until just beginning to brown around the edges. Rotate from top to bottom and front to back halfway through baking. Let cool completely on the cookie sheets.
There are multiple ways to distribute the dulce de leche. I chose to use a tiny cookie scoop to dollop the dulce de leche and the underside of a spoon to smooth it out. You can also use 2 spoons or a pastry bag. Aim for 2-4 teaspoons of dulce de leche--with such a wide range being suggested to accommodate individual tastes (and using less for thinner cookies and more for thicker).
I chose to sprinkle the dulce de leche with flaky sea salt before adding the top cookie to form a sandwich. I think the bite of salt keeps things more interesting and from being too sweet. The salt is not, as far as I know, traditional, so do whatever sounds good to you--or make 2 cookies and do a side by side taste test.
I am happy to report these cookies were still amazing without the vanilla, but do use it! If you do not have ground vanilla beans, you can also use the beans scraped out of a vanilla pod.