Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the all-purpose flour, unsweetened cocoa powder, 1 cup granulated sugar, baking powder, baking soda, and salt until well combined.
In a separate medium bowl, whisk together the buttermilk, vegetable oil, eggs, and 1 teaspoon vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently fold together with a spatula until just combined. Do not overmix.
In a small bowl, beat the softened cream cheese with 1/4 cup granulated sugar, egg yolk, and 1/2 teaspoon vanilla extract until smooth and creamy.
Fill each muffin liner halfway with the chocolate batter.
Add about 1 tablespoon of the cream cheese mixture into the center of each muffin.
Top each muffin with the remaining chocolate batter until the liners are about 3/4 full.
Use a toothpick or skewer to gently swirl the cream cheese filling into the chocolate batter for a marbled effect.
Bake in the preheated oven for 18 to 20 minutes, or until a toothpick inserted into the chocolate part comes out clean.
Remove from the oven and allow the muffins to cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.