Make the sauce:
Bring 1/4 cup water, the brown sugar and salt to a boil in a small saucepan, stirring until the sugar dissolves. Whisk in the cocoa powder until smooth. Remove from the heat and stir in the butter and vanilla. (You can refrigerate the sauce, covered, up to 3 days; reheat before serving.)
Make the sopaipillas:
In a large bowl, combine flour, baking powder and salt. Cut in shortening until mixture resembles fine crumbs. Gradually add water, tossing with a fork until a loose ball forms (dough will be crumbly).
On a lightly floured surface, knead the dough for 3 minutes or until smooth. Cover and let rest for 10 minutes. Roll out into a 12-in. x 10-in. rectangle. Cut into 12 squares with a knife or cut into 12 circles using a round biscuit cutter.
In a deep-fat fryer, heat 2 in. of oil to 375°. Fry sopaipillas for 1-2 minutes on each side. Drain on paper towels; keep warm.
Sprinkle with sugar, and drizzle with chocolate sauce for serving.