Preheat your oven to 350°F (175°C) and lightly grease the donut pan.
In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, salt, and nutmeg.
In a separate bowl, combine the milk, melted butter, eggs, and vanilla extract, whisking until smooth.
Pour the wet ingredients into the dry ingredients and mix until just combined; do not overmix.
Transfer the batter to a piping bag or use a spoon to fill each donut cavity about halfway full.
Bake in the preheated oven for 12-15 minutes until the donuts are lightly golden and spring back when touched.
Let the donuts cool in the pan for 5 minutes, then transfer them to a cooling rack.
Once cooled, use a piping bag to fill each donut with fruit jam. Insert the nozzle into the side of the donut to fill without breaking it.
Dust the filled donuts with powdered sugar if desired, then serve and enjoy!