Preheat oven to 350°F (175°C). Grease a donut pan.

Mix dry ingredients: In a large bowl, whisk together flour, sugar, baking powder, and salt.

Combine wet ingredients: In another bowl, whisk milk, egg, melted butter, and vanilla.

Make the batter: Gradually add the wet ingredients to the dry ingredients and mix until just combined. Gently fold in the raspberries.

Fill the donut pan: Spoon or pipe the batter into the donut cavities, filling them about ¾ full.

Bake for 12-15 minutes, or until the donuts are lightly golden and spring back when touched. Let cool in the pan for 5 minutes, then transfer to a wire rack.

Prepare the glaze: Whisk together powdered sugar, mashed raspberries, and milk (or lemon juice) until smooth.

Glaze the donuts: Dip each donut into the glaze, allowing excess to drip off. Let them set for a few minutes before serving.