Preheat your oven to 350°F (175°C). Generously spray two 6-cavity donut pans with nonstick cooking spray, making sure to coat the center posts thoroughly.

In a large mixing bowl, whisk together the flour, granulated sugar, baking powder, salt, and nutmeg until evenly distributed with no lumps.

In a separate medium bowl, whisk the eggs until slightly foamy, then add the milk, melted butter, and vanilla extract. Whisk until smooth and fully combined.

Pour the wet ingredients into the dry ingredients and gently fold with a spatula just until no dry flour remains visible. The batter will be thick but pourable—do not overmix or the donuts will be dense.

Transfer the batter to a large zip-top bag or piping bag. Snip off one corner and pipe batter into each donut cavity, filling about two-thirds full to allow room for rising.

Bake for 10-12 minutes, until the tops spring back when lightly touched and a toothpick inserted comes out clean. Let cool in the pans for 5 minutes, then carefully turn out onto a wire cooling rack to cool completely.

Make the glaze by whisking together the powdered sugar and 5 tablespoons milk in a medium bowl until smooth and glossy. Add more milk one teaspoon at a time if needed—the glaze should slowly drip off a spoon.

Divide the glaze into three bowls: leave one white, tint one red with gel food coloring, and one blue. Dip the top of each cooled donut into the white glaze, letting excess drip off, then place on the wire rack.

Once the white glaze sets (about 15 minutes), drizzle red and blue glazes over the donuts in stripes or zigzags using squeeze bottles or small zip-top bags with a corner cut. Add patriotic sprinkles immediately before the colored glaze sets.

Let the decorated donuts stand for 20-30 minutes until all glaze layers are completely set and no longer tacky to the touch before serving or storing.