Preheat the oven to 350ºF. Add the sugar, milk, oil, egg, and vanilla extract to a mixing bowl and stir well.
In a separate mixing bowl, add the flour and baking powder, and salt.
Combine the wet and dry ingredients together.
In another bowl, combine the strawberries and 2 tbsp flour.
Gently add the strawberries to the batter and transfer to a 9x5-inch loaf pan.
Bake in the oven for 50 minutes, then remove and cool for 10 minutes before transferring to a wire cooling rack. In the meantime, combine the powdered sugar, extract, and strawberries in a small bowl to make the glaze. Add cream or milk one tablespoon at a time until you reach a good consistency.
When the bread is completely cooled, drizzle the glaze on top.