In a large bowl, mix the sourdough starter, melted butter, and milk until smooth.
In a separate bowl, whisk together flour, sugar, salt, baking powder, and spices.
Gradually add the dry mixture to the wet ingredients, mixing until combined.
Add eggs and vanilla extract and mix until a soft dough forms.
Turn the dough onto a floured surface and knead for 5 minutes until smooth.
Place dough in a greased bowl, cover, and refrigerate overnight.
Remove dough from the fridge and let it rest at room temperature for 1 hour.
Roll the dough to ½-inch thickness on a floured surface.
Use a donut cutter to cut out the donut shapes.
Place donuts on a parchment-lined baking sheet and let rise for 1-2 hours.
Preheat the oven to 375°F and bake the donuts for 12-15 minutes until golden.
For the glaze, whisk together powdered sugar, milk, and vanilla until smooth.
Dip warm donuts in the glaze and let it set on a wire rack.