Using stand mixer fitted with paddle, mix flour, superfine sugar, and salt on low speed until combined.
Add butter, 1 piece at a time, and mix until crumbly, 1 to 2 minutes.
Add cream cheese and vanilla and beat until mixture begins to form large clumps.
Knead dough by hand, just until it forms cohesive mass. Divide dough in half, form each half into disk, wrap disks in plastic wrap, and refrigerate for 30 minutes.
Adjust oven rack to middle position and heat oven to 375°.
Line 2 baking sheets with parchment paper. Roll each disk of dough 1/8 inch thick; refrigerate for 10 minutes.
Using 1 3/4 inch cookie cutter, cut dough, gathering and rerolling scraps once; space cookies 1 1/2 inches apart on prepared sheets.
Bake 1 sheet at a time, until light golden brown, about 10 minutes, rotating sheet halfway through baking.
Let cookies cool on sheet for 3 minutes, then transfer to wire rack and let cool completely.
Microwave dulce de leche in bowl at 50 percent power for 20 seconds. Sir in sea salt.
Spread bottoms of half of cookies evenly with warm dulce de leche, then top with remaining cookies, pressing lightly to adhere.
Dust cookies with confectioners sugar before serving.