Heat the oven to 375°F (190°C). Line a 12-cup muffin pan with paper liners or grease the pan well.

Combine 1/2 cup flour and 1/4 cup sugar for the crumb topping. Cut in the cold butter with your fingers or a pastry cutter until coarse crumbs form, then set aside.

Whisk 2 cups flour, 1 cup sugar, baking powder, and salt in a large bowl. In a second bowl, whisk the eggs, oil, milk, and vanilla until blended.

Add the wet mixture to the dry mixture and stir just until combined. A few small lumps are fine, and overmixing should be avoided.

Gently fold in the blueberries. If using frozen blueberries, add them while still frozen and fold carefully to reduce streaking.

Divide the batter among the muffin cups, filling each about three-quarters full. Sprinkle the crumb topping evenly over every muffin.

Bake for 20 to 25 minutes, until golden and a toothpick inserted in the center comes out clean or with a few moist crumbs. If using frozen blueberries, the muffins may need roughly 2 to 3 additional minutes.

Cool the muffins in the pan for about 5 minutes, then transfer them to a wire rack.