In a large mixing bowl, combine flour, sugar, salt and baking powder and mix well. Add shortening and break it up by hand until it resembles cornmeal. Add chicken stock and knead until all is incorporated. Let it rest, covered, for at least 30 minutes in cooler.
Meanwhile, make the filling. Combine blackberries, strawberries, goat cheese and sugar and mix well.
When the dough has chilled, roll it out to 1/4-inch thickness on a lightly floured surface with a rolling pin. Cut circles out of the dough with a 4-inch round cutter. Spoon a heaping tablespoon of filling into the center of each dough circle. Beat the eggs and water together in a small bowl. Brush the egg wash all around the edges of the dough. Fold the dough over the filling to make the circles into half moons. Crimp the edges with the tines of a fork to seal the dough closed.
Heat a pan, filled half way up with peanut oil, to 350 degrees F.
Fry the empanadas until golden brown, about 6 to 8 minutes, turning them over occasionally with tongs.