In a large bowl, whisk together the cake flour, granulated sugar, baking powder, baking soda, salt, and nutmeg until well combined.

In a separate medium bowl, whisk the melted butter with the egg. Then, whisk in the buttermilk and vanilla extract until smooth.

Pour the wet ingredients into the dry ingredients. Use a spatula to gently fold until just combined, being careful not to overmix. Gently fold in the blueberries.

Turn the sticky dough out onto a large piece of floured plastic wrap. Pat it into a 1/2-inch thick disc, wrap tightly, and refrigerate for at least 1 hour or up to 2 hours. This step is crucial for handling.

Unwrap the chilled dough onto a well-floured surface. Use a 3-inch donut cutter to cut out donuts. Gently re-roll scraps once to cut more. Place the cut donuts and holes on a parchment-lined baking sheet.

Pour oil into a heavy-bottomed pot to a depth of 2-3 inches. Heat over medium heat to 365-375°F (185-190°C), using a thermometer to monitor the temperature.

Carefully place 2-3 donuts at a time in the hot oil. Fry for 60-90 seconds per side, until deep golden brown. Use a spider strainer to transfer them to a wire rack set over a baking sheet to drain. Let the oil return to temperature between batches.

While the donuts are still warm, whisk the powdered sugar and 3 tablespoons of milk in a shallow bowl until smooth. Add more milk, 1 teaspoon at a time, if needed to reach a thin dipping consistency. Dip the top of each warm donut into the glaze, let the excess drip off, and place back on the wire rack to set.