Preheat the oven to 180'C / Fan 160'C / Gas 4 and grease a 12-hole muffin tin with oil (top tip: I find the silicone muffin trays much easier for this!)
Add the flour, sugar and baking powder to a large mixing bowl and stir together with a wooden spoon.
In a separate bowl, add the milk, oil, egg and vanilla extract and gently whisk together with a work until combined.
Pour the liquid ingredients into the dry ingredients and use a whisk to mix together until it forms a runny batter with no lumps.
Pour the batter evenly between the muffin tin holes so they are all about half full.
Bake the doughnuts in the oven for 15-20 minutes until well-risen and golden brown on top. Remove from the oven and place the tins on a cooling rack until you can handle them, then turn them out of the tin while still warm.
Brush the melted butter over each doughnut and then roll in the granulated sugar so they are liberally coated.
Spoon the jam into a piping bag fitted with a small round nozzle. Gently press the nozzle into the bottom the doughnut and then pipe in the jam until it starts to feel full. Continue with all the doughnuts and then tuck in and enjoy!
Notes
These doughnuts are best eaten fresh from the oven while still warm. They will keep for a couple of days and can be refreshed with a 10-second zap in the microwave before eating.
For a dairy free recipe use almond milk instead of milk and dairy-free spread instead of butter.