Preheat the oven to 180°C (350°F). 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 bowl, beat the eggs with the plain yogurt, vegetable oil, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently mix until just combined, being careful not to overmix.
Divide the batter into two equal portions. To one portion, add the unsweetened cocoa powder and milk, and gently fold until the cocoa is fully incorporated.
Spoon the plain batter and the cocoa batter alternately into the muffin cups to create a bicolored effect, filling each cup about two-thirds full.
Using a skewer or toothpick, swirl the two batters gently 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 them to a wire rack to cool completely.