Preheat oven to 350°F (180°C) and grease a donut pan.
In a bowl, whisk together flour, sugar, baking powder, and salt.
In another bowl, whisk milk, egg, melted butter, vanilla, and strawberry puree.
Combine wet ingredients into dry ingredients and stir until just mixed.
Pipe or spoon the batter into donut pan cavities about 3/4 full.
Bake donuts for 10 to 12 minutes, until they spring back when touched.
Let donuts cool in the pan for 5 minutes, then remove to a wire rack.
Prepare glaze by mixing powdered sugar, strawberry puree, and vanilla until smooth.
Dip the tops of cooled donuts into the glaze and let set before serving.