In an electric mixer, fitted with paddle, cream the shortening and sugar. Add the eggs, 1 at a time and beat until incorporated. With the machine running, slowly add the buttermilk. Switch the paddle attachment to a dough hook and add the blueberries. Sift together the flour, salt, baking powder and baking soda. Add the flour mixture, 1 cup at a time, until the dough forms a smooth ball and climbs up the dough hook. Place the dough in a greased bowl, turning once and cover with plastic wrap. Refrigerate for 1 hour. Preheat the fryer to 350 degrees. Turn the dough out onto a floured surface and roll out to 1/2-inch thick. Using a doughnut cutter or 2 biscuit cutters, cut the dough into rounds. Fry the doughnuts in batches until golden brown. Remove and drain on paper towels. In small bowl, whisk together the milk and powdered sugar. Drizzle the glaze over each doughnut and allow to sit until the glaze sets. Serve the doughnuts on a platter.