Prepare the dough: In a bowl, dissolve yeast and 1 tablespoon sugar in warm milk. Let sit until frothy, about 5 minutes. Add flour, salt, melted butter, egg, and remaining sugar. Knead until smooth. Let rise until doubled.
Form and fry donuts: On a floured surface, roll out dough to 1/2 inch thickness. Cut out donuts and let rise again. Fry in 375°F (190°C) oil until golden. Drain on paper towels.
Make the filling: Beat cream cheese, powdered sugar, and vanilla until smooth. Fold in strawberry jam.
Fill donuts: Once cooled, make a hole in the side of each donut. Pipe in the strawberry cheesecake filling.
Glaze: Mix powdered sugar, milk, and vanilla. Drizzle over filled donuts.
