Preheat oven to 375°F. Grease a 12-cavity donut pan.
Whisk flour, sugar, baking powder, salt, and nutmeg in a large bowl.
Whisk milk, yogurt, eggs, melted butter, and vanilla in a separate bowl until smooth.
Fold wet ingredients into dry just until combined. Avoid overmixing; the batter should be thick.
Pipe or spoon batter into the pan, filling each well about two-thirds full.
Bake 10–12 minutes, until the tops spring back and edges are lightly golden.
Cool donuts in the pan 5 minutes, then transfer to a rack to cool completely.
Simmer blueberries and lemon juice in a small saucepan over medium heat for 3–4 minutes, stirring and mashing until juicy.
Strain the mixture through a fine sieve to remove skins. Let the blueberry juice cool 5 minutes.
Whisk powdered sugar with the blueberry juice, vanilla, and a splash of milk to a thick, pourable glaze.
Dip cooled donuts into the glaze, letting excess drip off. Set on a rack to firm up; double-dip for extra color.