Preheat the oven to 350°F. Lightly spray a 9x5-inch loaf pan with baking spray.
In a medium bowl, whisk together the sugar, milk, oil, egg, and vanilla. In another medium bowl, stir together 2 cups of flour, baking powder, and salt. Add the flour mixture to the sugar mixture and stir until just combined.
In a small bowl, combine strawberries and 2 tablespoons flour, tossing to coat strawberries. Fold the strawberries into the batter. Pour the batter into the prepared loaf pan.
Bake for 55 to 60 minutes or until a wooden pick inserted into the center comes out clean. Let the bread cool in the pan for 10 minutes. Remove the bread from the pan and cool completely on a wire rack.
Place the strawberries in a small bowl and mash. Stir in the powdered sugar and milk. Spoon over the cooled bread. Let stand for 30 minutes or until the glaze sets before serving.
