Preheat oven to 350°F (175°C). Line 12 standard muffin cups with paper liners.
Combine the oats and buttermilk. Let stand for 10 minutes.
Using an electric mixer on medium speed, beat the cream cheese, sugar, and vanilla until combined. Set aside.
Whisk together the flour, brown sugar, baking powder, baking soda, and salt.
Add the egg and melted butter to the oat mixture, stirring until combined. Add to the flour mixture, stirring just until combined. Gently stir in the cherries.
Place about 2 tablespoons of muffin batter in each muffin cup. Top with 1 & 1/2 to 2 tablespoons of the cream cheese filling. Then, top with the remaining muffin batter. (The cups will be almost full.)
Bake 25 to 30 minutes, or until a toothpick inserted into the center comes out clean.