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 yogurt, vegetable oil, eggs, and vanilla extract until smooth.
In a separate bowl, sift together the flour, baking powder, baking soda, salt, and sugar.
Gradually add the dry ingredients to the wet ingredients and mix until just combined, being careful not to overmix.
Divide the batter evenly into two bowls.
Add the cocoa powder to one bowl and gently fold it into the batter until fully incorporated.
Spoon a tablespoon of the plain batter into each muffin cup, then add a tablespoon of the cocoa batter on top.
Use a skewer or knife to gently swirl the two batters together to create a marbled effect.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the tin for 5 minutes before transferring to a wire rack to cool completely.