Preheat the oven to 400°F and line a standard 12 cup muffin pan and a 6 cup muffin pan with paper liners, for a total of 18 muffins.
Make the streusel topping by combining 1 cup flour, 2/3 cup granulated sugar, 1 teaspoon cinnamon, and 1/4 teaspoon salt in a medium bowl.
Pour in the melted butter and mix with a fork until the mixture forms moist, crumbly clumps, then set aside.
Make the cheesecake filling by beating the softened cream cheese, 1/4 cup granulated sugar, and vanilla bean paste in a small bowl until completely smooth, then set aside.
Make the muffin batter by whisking together 2 1/4 cups flour, 1/2 cup granulated sugar, 1/4 cup light brown sugar, 1 1/2 teaspoons baking powder, 1/4 teaspoon baking soda, 1 1/2 teaspoons cinnamon, 3/4 teaspoon ground ginger, and 3/4 teaspoon salt in a large bowl.
In a separate bowl, whisk the eggs, water, and vegetable oil until well combined.
Pour the wet mixture into the dry ingredients and stir just until no dry streaks of flour remain.
Fold in the grated carrots until evenly distributed in the batter.
Spoon muffin batter into each lined cup, filling each about one third full.
Add about 1 heaping teaspoon of cheesecake filling into the center of each muffin cup, keeping the filling away from the sides.
Cover the cheesecake filling with more muffin batter until each cup is about two thirds to three quarters full.
Sprinkle the streusel topping evenly over the tops of the muffins, pressing lightly so it adheres.
Bake for 18 to 20 minutes, or until the tops are golden and a toothpick inserted into the muffin near the edge (avoiding the cheesecake center) comes out clean.
Remove the muffins from the oven and let them cool in the pans for 10 minutes.
Transfer the muffins to a wire rack to cool completely.
Make the glaze by stirring together the milk and powdered sugar in a small bowl until smooth.
Drizzle the glaze over the cooled muffins before serving.