Preheat your oven to 350°F (175°C). Line a muffin tin with paper liners.
In a large bowl, whisk together the flour, sugar, brown sugar, baking powder, baking soda, and salt.
In another bowl, mix the grated zucchini, vegetable oil, eggs, and vanilla extract.
Combine the wet ingredients with the dry ingredients until just mixed.
In a separate bowl, beat the cream cheese, sugar, and vanilla extract until smooth.
Fill each muffin cup halfway with the zucchini batter. Add a spoonful of the cream cheese mixture, then top with more zucchini batter.
Bake for 20-25 minutes or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 10 minutes, then transfer to a wire rack to cool completely.