Preheat your oven to 400 degrees F. Cupcake cake liners to line the cups of a muffin tin. Grease the inside of the liners with non-stick cooking spray.
Place cream cheese in a microwave-safe bowl and heat on low power for 40 seconds until softened. Beat in 1/4 cup sugar until smooth. Set aside the filling while you make the muffin batter.
Whisk together the flour, sugar, brown sugar, baking powder, baking soda, ground cinnamon, ground ginger, and salt in a large mixing bowl. Set aside.
Whisk the eggs, water, and vegetable oil together in a small mixing bowl. Pour the wet ingredients into the dry ingredients and mix until evenly combined.
Add the grated carrots and fold them into the muffin batter.
Add about 1 1/2 tablespoons of muffin batter in each muffin cup and spread it out to cover the bottom. Drop 1 heaping tablespoon of cream cheese filling on top of the muffin batter. Cover the cream cheese filling with enough muffin batter so that muffin cups are full.
Sprinkle raw sugar on top of each muffin, if desired.
Bake for 16-20 minutes until a toothpick inserted in the top of a muffin comes out clean and the tops feel firm to the touch.
Remove the muffins from the oven, and immediately transfer them to a wire rack. Cool for at least 30 minutes to give the filling time to set up. Serve warm or at room temperature.