In a mixer fitted with the paddle attachment, beat together the butter and sugar at medium-high speed until it is pale and fluffy, about 5 minutes. Stir in the vanilla extract.
Combine the flour and salt, add to the creamed butter at once, then stir with a wooden spoon or spatula for a couple of turns. Return to the stand and mix on low speed until the flour is incorporated, do not over mix. Divide the dough into 6 equal pieces, and cover each in plastic wrap. Refrigerate until very firm, at least 2 hours or overnight.
Place one portion of dough between 2 pieces of parchment or wax paper and roll out to a flat disc shape about 1/8-inch thick and 7 inches wide (see cook's note). Return the rolled discs to the refrigerator between layers of parchment and chill until firm again, 15 to 20 minutes.
Preheat the oven to 350 degrees F. Line 2 large baking sheets with parchment paper or nonstick liner. Working in batches, place chilled discs on prepared baking sheets (2 per sheet) and set them in the upper and lower oven racks. Bake them for 12 to 14 minutes, rotating the pans halfway through so they color evenly, until lightly golden.
Cool on the baking sheets for 10 minutes before removing to a wire rack. The alfajores will firm up as they cool and should release easily from the liner before transferring.
Place one alfajor on a serving plate and spread evenly with 1/4 cup of dulce de leche. Top with the next alfajor and repeat with remaining layers. Cover top layer with toasted coconut. Serve with extra coconut on the side, whipped cream or ice cream.
For more evenly sized discs, draw a 7-inch circle on parchment or wax paper. Use this sheet as a guide when rolling out the discs. Trim the dough as needed and re-roll the scraps into the remaining dough to make more discs.