Prepare the Dough: Mix warm milk and yeast in a small bowl; let sit for 5-10 minutes until foamy. In a large bowl, combine sugar, melted butter, egg, and salt, then stir in the yeast mixture. Gradually add flour and knead for 8-10 minutes until smooth. Cover and let rise for 1 hour until doubled in size.
Shape and Proof: Roll the dough to ½-inch thickness on a floured surface. Cut into 3-inch rounds, place on a parchment-lined tray, cover, and let rise for 30-40 minutes until puffy.
Fry the Donuts: Heat 2-3 inches of oil to 350°F (175°C). Fry donuts in batches for 1-2 minutes per side until golden. Drain on a paper towel-lined plate.
Coat the Donuts: While warm, roll in a cinnamon-sugar mixture (if using). Let cool completely before filling.
Make the Filling: Beat cream cheese, powdered sugar, and vanilla until smooth. Fold in strawberry preserves and diced strawberries. Transfer to a piping bag.
Fill the Donuts: Poke a small hole in each donut, insert the piping bag, and fill until slightly plump. Serve immediately or refrigerate for a chilled filling.