Preheat oven to 425 degrees. Line a standard 12-count muffin pan with cupcake papers then set aside.
Add brown sugar, granulated sugar, oil, eggs, sour cream, vanilla and milk to a mixing bowl then whisk vigorously until combined.
In a separate bowl. sift together flour, baking soda, baking powder and salt.
Add dry ingredients to wet then stir with a wooden spoon until just moistened and flour is still visible. Do not overmix.
Add 3/4 cup of raspberries to batter then gently stir until just combined.
Distribute batter evenly among 12 muffin liners.
Top muffins with remaining 1/2 cup of raspberries.
Bake for 5 minutes at 425 degrees. Keeping the oven door closed, reduce temperature to 350 degrees then bake for 15 additional minutes or until a toothpick inserted into the center of a muffin comes out clean. Avoid overbaking.
Remove muffins from the oven and cool in the muffin pan for 5 minutes. After 5 minutes, remove muffins from the pan and place on a wire rack to cool to room temperature.
Drizzle muffins with melted white chocolate and enjoy.
Muffins will keep in an airtight container at room temperature up to 2 days.