In a large bowl of a mixer, combine the sugars, flour cocoa powder, baking soda, salt and chile powder. Mix at low speed for a minute or two until all ingredients are combined.
Mix in the butter a piece at a time until the butter is thoroughly incorporated.
Add the egg and the vanilla and continue to mix until a dough begins to form.
Turn the dough out onto a board and form it into a disk. Wrap in plastic wrap and refrigerate for at least one hour or overnight until firm.
When you are ready to bake the cookies, let the dough warm up for 5 - 10 minutes. Line 3 sheet pans with parchment paper. Cut the dough in half and roll one half out until it is approximately ⅛ inch thick. Using a 2 inch round cookie cutter, cut rounds out and place on a parchment lined sheet pan.
Place the rounds on the sheet pan. Repeat with the remaining dough. Bake for 12 - 15 minutes until cookies are dry. Let cool.
When cookies have cooled, stir the dulce de leche and spread about a tablespoon on the bottom of one cookie. Top with another cookie and "squish" until the filling reaches the edge. Repeat with remaining cookies.
Store in an airtight container.