Place apricots in a saucepan, and add water to cover. Bring to a boil. Reduce heat to low and simmer for 30 minutes, or until tender. Drain, reserving 5 tablespoons liquid.
Place apricots and reserved liquid in a food processor container fitted with steel blade. Process until smooth. Add sugar, butter, and cinnamon; process until blended.
Roll out one crust on lightly floured surface and cut it into six 4 inch squares. Place 1 tablespoon apricot filling in the center of each square. Fold each square in half diagonally to form a triangle. Press a fork dipped in flour onto the edges to seal, and poke tops to permit steam to escape. Repeat with remaining crust and apricot mixture.
Heat oil in a large skillet on medium-high heat. Cook triangles, a few at a time, 2 to 3 minutes on each side; fry until the crust is golden brown. Drain on paper towels. Sprinkle with confectioners' sugar.