This is how I make the alfajores that I remember eating in Argentina way back in '72 and '73.
Overview: Make 2" round sugar cookies, fill with thickened sweetened condensed milk (dulce de leche), roll edges in finely chopped coconut (you may have to add some dulce de leche to the edges before rolling). Remember you're making two cookies for each alfajore.
Ethel's Sugar Cookies - from Betty Crocker's Cooky Book (makes about 4 doz. 3" cookies)
3/4 c shortening (part butter or margarine)
1 c sugar
1 t vanilla
2 1/2 c all-purpose flour
1 t baking powder
1 t salt
Mix shortening, sugar, eggs, and flavoring thoroughly. Measure flour by dipping method or by sifting. Stir flour, baking powder, and salt together, blend in. Chill at least 1 hr. (I never chill the dough).
Heat oven to 400 degrees (mod. hot). Roll dough 1/8" thick (I roll it thicker, a scant 1/4") on lightly floured board. Cut with cooky cutter. Place on ungreased baking sheet (I use parchment). Bake 6 to 8 minutes (these bake quickly so watch carefully) or until cookies are a delicate golden color.
Dulce de Leche
Place one can of sweetened condensed milk in a medium sized pan sideways and cover with water by 1/2" or so. Bring to a boil and then turn down to a simmer. Cover and let simmer about 2 hours. Check the water lever periodically to make sure the can is always covered with water.
Finely chop coconut in food processor or with a knife.
I store them in a Tupperware to soften up, that's when they're the best and don't crack when eaten.