Preheat the Oven: Preheat the oven to 350°F. Line a 12-cup muffin tin with paper liners and set aside.
Make the Filling: In a medium mixing bowl, beat the softened 1 8-ounce package cream cheese, softened, 1/2 cup packed light brown sugar, and 1 large egg until smooth and creamy. Stir in the 3/4 cup mini chocolate chips and set aside.
Make the Batter: In a large mixing bowl, whisk together the 1 cup all-purpose flour, 1/2 cup granulated sugar, 1/4 cup packed light brown sugar, 1/3 cup unsweetened cocoa powder, and 1 teaspoon baking soda. Add the 3/4 cup buttermilk and 1/4 cup vegetable oil and whisk until the batter is smooth and no dry streaks remain.
Fill the Cups: Divide the chocolate batter evenly among the 12 muffin cups, filling each about halfway. Spoon about 2 heaping tablespoons of the cream cheese mixture onto the center of each cupcake, pressing gently so it sinks slightly into the batter.
Bake: Bake for 18 to 20 minutes, or until the chocolate portion of the cupcakes is set and a toothpick inserted into the cake comes out clean.
Cool: Remove from the oven and let the cupcakes cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
Notes
Make-Ahead: Cupcakes can be baked a day in advance. Store them tightly covered at room temperature or refrigerated. Storage: Keep in an airtight container at room temperature for up to 3 days, or refrigerate for up to 1 week.Freezing: Wrap each cupcake individually in plastic wrap and freeze in a bag or airtight container for up to 3 months. Thaw at room temperature or microwave on half power until warmed through.Reheating: These cupcakes are delicious cold, but if you like them warm, microwave briefly on medium power for a melty center.