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.
