Preheat the oven to 400°F. Lightly grease a standard 12-well muffin pan. Or line the pan with paper muffin cups, and grease the cups.
To make the filling: Place the cream cheese in a microwave-safe bowl, and heat on low power for 40 seconds. Stir in the sugar and flavor. Set aside.
To make the muffin batter: In a medium-sized bowl, whisk together the dry ingredients.
In a small bowl, whisk together the eggs, water, and oil.
Stir the wet ingredients into the dry ingredients.
Fold in the grated carrots, stirring to combine.
Drop about 2 tablespoons of the batter into each muffin cup, spreading it to cover the bottom.
Dollop on a heaping tablespoon of filling.
Cover with enough batter to fill the muffin cups quite full.
Sprinkle the tops of the muffins with coarse white sparkling sugar, if desired.
Bake the muffins until a toothpick inserted into the cake part of one comes out clean, about 20 minutes.
Remove the muffins from the oven, and as soon as you're able to handle them, transfer them to a rack.
