In a mixing bowl, combine the strawberries and 1/2 cup sugar. Using a fork, lightly mash the berries. Cover and refrigerate for 1 hour. Preheat the oven to 375 degrees F. Grease a baking sheet with 1 teaspoon of the butter. In a mixing bowl, sift 1 3/4 cups of the flour, cocoa, salt and baking powder together. Add the remaining 1/4 cup sugar and mix well. Add the remaining 1/2 cup butter and work it into the dry ingredients, using your hands, until the mixture resembles coarse crumbs. Fold in the chocolate milk. The dough will be sticky. Dust your work surface with 1 tablespoon of the flour. Turn the dough onto the floured surface. Gently fold each side towards the center. Pick up the dough and dust the work surface with the remaining tablespoon flour. Return the dough to the floured surface and fold each side towards the center again. Turn the dough over and lightly press it out to 1-inch thickness. Cut the biscuits using a 2 1/4-inch round cookie cutter. Place them on the baking sheet and bake until golden, about 30 minutes. Remove from the oven and cool completely. To assemble, cut the biscuits in half. Place a scoop of the ice cream in the center of each biscuit. Place the shortcakes in the center of each plate. Spoon the strawberries over the shortcakes. Garnish with powdered sugar and serve immediately.