In a stand mixer bowl, combine warm milk and 1 tablespoon of sugar; sprinkle yeast over the top and let sit for 5 minutes until foamy.

Add the remaining sugar, eggs, melted butter, and salt; mix with the paddle attachment until combined.

Switch to the dough hook and gradually add flour, kneading on medium-low speed for 5 to 7 minutes until the dough is smooth and pulls away from the sides.

Transfer dough to a lightly greased bowl, cover with plastic wrap, and let rise in a warm, draft-free area for 90 minutes or until doubled in size.

Punch down the dough and roll out on a floured surface to 1/2-inch thickness.

Cut into rounds using a 3-inch donut cutter and place on a parchment-lined baking sheet.

Cover and let the cut donuts rise for an additional 30 to 45 minutes.

Heat vegetable oil in a heavy-bottomed pot or Dutch oven to 350°F (175°C).

Carefully fry donuts in batches for 60 to 90 seconds per side until golden brown, then transfer to a wire rack to cool slightly.

Prepare the glaze by whisking strawberry puree, powdered sugar, and vanilla extract in a shallow bowl until smooth.

Dip the tops of the warm donuts into the glaze and allow them to set on the rack for 10 minutes before serving.