Prepare Blueberries: Place frozen blueberries in a microwave-safe bowl and microwave for 1 to 2 minutes until defrosted. Let them cool to room temperature for about 3 to 5 minutes without draining the juice.

Mix Dry Ingredients: In a small bowl, whisk together flour, baking powder, and salt until combined.

Combine Wet Ingredients: In a large mixing bowl, add the cooled blueberries with their juice, sugar, and vegetable oil. Whisk until thoroughly combined, then add in the egg whites, lemon zest, and vanilla extract, mixing until fully incorporated.

Incorporate Dry Ingredients: Gradually add the flour mixture to the wet ingredients in two batches, stirring just until combined. Cover the dough and refrigerate for at least 2 hours to firm up.

Preheat and Prepare Baking Sheets: Preheat the oven to 400°F (200°C). Line two baking sheets with parchment paper.

Form and Coat Cookies: Place white sugar and powdered sugar in separate small bowls for coating. Scoop 1½ tablespoons of dough and shape it into a ball. Roll the dough ball in white sugar first, then in powdered sugar until fully coated. Place the cookie dough balls on the prepared baking sheet, spacing them 1½ inches apart.

Bake: Bake the cookies for 8 to 10 minutes, switching racks halfway through for even baking, until the cookies are just set. Cool on the baking sheet briefly, then transfer to a wire rack to cool completely.