Mix sourdough starter, milk, sugar, butter, eggs, and vanilla in mixer.
Add flour, salt, nutmeg; knead 5–6 mins until smooth and elastic.
Let rise 2 hours at room temp, then refrigerate overnight.
Roll dough to ½-inch thickness, cut with 3" cutter and donut hole cutter.
Proof for 1–2 hours until puffy and risen.
Fry in 350°F oil for 1–2 minutes per side until golden.
Drain on paper towels; let cool slightly.
Whisk glaze ingredients; dip donuts or roll in cinnamon sugar.