Preheat oven to 350° and line a muffin tin with cupcake liners or parchment squares. In a small bowl, beat together the cheesecake filling ingredients until smooth and set aside.
Using a stand mixer or a large bowl, cream together the first five muffin ingredients through the red coloring. Beat in the eggs, then the sour cream and buttermilk. In a separate bowl, whisk together the dry ingredients, then gradually add that mixture to the batter, scraping the sides of the bowl between additions.
Fill each liner about halfway with batter, then place a scoop of cheesecake filling on top. Cover the filling with the rest of the batter. This recipe make 12-15 muffins, depending on how full you fill the liners. Bake for 25-27 minutes, then remove from oven and let the muffins cool in the pan for about 15 minutes.
While the muffins cool, prepare the icing by whisking together the powdered sugar, milk, and vanilla. Drizzle the icing over the tops of the muffins and serve warm.