Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Melt shortening and 1/2 cup butter in a small pan over low heat; pour melted mixture into a mixing bowl. Stir cocoa into butter mixture until well combined, followed by sugar. Dissolve 4 teaspoons instant coffee with hot water in a small bowl; stir into cocoa mixture.
Whisk eggs into batter, one at a time, beating each egg in thoroughly before adding the next. Stir flour, 2 teaspoons vanilla extract, and salt into batter just until moist.
Pour batter into prepared baking pan.
Bake brownies in the preheated oven until a toothpick inserted into the center comes out with moist crumbs, 25 to 30 minutes. Cool completely.
Beat 1/2 cup softened butter with 1 teaspoon vanilla extract in a bowl.
Add confectioners' sugar to mixture and beat until creamy using an electric mixer on medium speed. Dissolve 1 tablespoon instant coffee with milk in a small bowl; add to frosting. Increase mixer speed to high and beat until light and fluffy, 3 to 5 minutes. Frost cooled brownies.