Preheat the oven to 180°C (350°F) and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the all-purpose flour, granulated sugar, baking powder, baking soda, and salt until well combined.
In a separate medium bowl, whisk the plain yogurt, vegetable oil, eggs, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined, being careful not to overmix.
Divide the batter evenly into two bowls.
Add the unsweetened cocoa powder and milk to one bowl and gently fold until the cocoa is fully incorporated and the batter is smooth.
Spoon a tablespoon of the plain batter into each muffin cup, then add a tablespoon of the cocoa batter on top. Repeat layering until the muffin cups are nearly full, creating a bicolored effect.
Using a skewer or toothpick, gently swirl the batters together in each muffin cup to create a marbled pattern.
Bake in the preheated oven for 18 to 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and allow them to cool in the tin for 5 minutes before transferring to a wire rack to cool completely.