Whisk together the flour, baking powder, granulated sugar, and salt in a large bowl. Beat the egg with the milk and vanilla in a separate bowl, then pour into the dry ingredients and stir until just combined with a few lumps remaining.

Fold in the blueberries and white chocolate chips gently with a spatula in 5 or 6 slow turns until evenly distributed.

Heat 2 inches of vegetable oil in a medium saucepan over medium to medium-high heat to 350°F (175°C). Scoop the batter in 1-tablespoon portions and fry in batches of 4 to 5 for 3 to 4 minutes, turning halfway, until deep golden brown all over.

Remove with a slotted spoon, drain on paper towels for 1 minute, then transfer to a serving plate and dust with the 2 tbsp powdered sugar through a fine-mesh sieve. Serve immediately.