Combine flour, yeast, sugar, egg, and milk in a mixer with a dough hook. Mix 1 minute until just combined, then add butter and salt. Knead 7–8 minutes until smooth and elastic.
Transfer dough to a greased bowl, cover with plastic wrap, and refrigerate overnight or let rise at room temperature until doubled.
Punch down the dough, roll out on a lightly floured surface, and cut into circles. Cut smaller circles in the centers for the donut holes. Place each donut on a parchment square, cover, and let rise until doubled again.
Heat oil in a deep pot to 330°F/165°C. Carefully transfer donuts from parchment to oil and fry until golden on both sides. Drain on paper towels.
While donuts cool, puree strawberries and whisk with powdered sugar until smooth. Decorate donuts with glaze and let set at room temperature.