In the bowl of an electric mixer, beat the dairy-free butter and sugar until smooth. Add the dairy-free yogurt and vanilla extract and beat until smooth.
Sift together the flour, baking powder and salt. Add a little at a time to the mixture with the wet ingredients, beating well between each addition. (Pro tip: be sure to turn the speed of the mixture way down as you are adding the flour mixture and only increase the speed once it's well combined. Otherwise, you will have flour all over your kitchen.)
Continue to beat the mixture until it pulls away from the sides of the mixer and dough forms.
Divide the dough in half. Form each half into a smooth ball and then flatten into a disc about 4.5 x 4.5 inches and 1 inch tall. Wrap each disc in plastic wrap and refrigerate for at least 1 hour until firm enough to roll out, or up to a day.
When ready to bake, preheat the oven to 350 degrees Fahrenheit. Line a baking sheet with parchment paper and set aside.
Roll out one of the discs of dough on a floured surface into a rectangle* about 1/8 inch thick. Sprinkle additional flour on the dough and/or surface and rolling pin if it starts to stick.
Cut the rectangle of dough into 2 1/2-inch squares.
Add 3/4 -1 teaspoon of Almond Apricot Filling (recipe follows) to the center of each square. Fold 2 opposite corners of each square over to meet in the middle and gently press down to seal. If you're having a hard time getting the corners to stick, add a teeny amount of filling between the two corners to act as a glue. Continue with the remaining disc of dough.
Bake for 10 to 12 minutes until lightly browned on the bottoms. Cool on a wire cooling rack until completely cool. Dust with powdered sugar if desired.