Whisk flour, sugar, baking powder, and salt until smooth and well combined.
Whisk milk, egg, vanilla, and melted butter in a separate bowl until blended.
Combine wet and dry ingredients, stirring gently until a soft dough forms; add flour if too sticky.
Roll the dough ½ inch thick and cut into donut shapes, then place on parchment.
Fry at 350°F for 1 to 2 minutes per side until golden and slightly puffed, then drain.
Cook strawberries, sugar, and lemon juice for 5 to 7 minutes until thick and jammy; let cool.
Beat cream cheese, powdered sugar, and vanilla, adding milk until thick and pourable.
Pipe strawberry filling into each donut through the side.
Dip tops into cheesecake glaze and let set before serving.