Preheat oven to 375°F (190°C) and line a muffin tin with paper liners.
In a large bowl, whisk together flour, granulated sugar, brown sugar, baking powder, baking soda, and salt.
In another bowl, mix milk, vegetable oil (or melted butter), eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently stir until just combined.
Fold in the raspberries and white chocolate chips carefully.
Divide the batter evenly among muffin cups, filling each about 3/4 full.
Sprinkle extra white chocolate chips or coarse sugar on top if desired.
Bake for 18–22 minutes, or until a toothpick inserted into the center comes out clean.
Allow muffins to cool for a few minutes before removing them from the pan.