Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups lightly.
In a large bowl, combine the rolled oats and Greek yogurt. Let the mixture sit for 5 minutes to soften the oats.
In a separate bowl, whisk together the sugar, eggs, vegetable oil, and vanilla extract until smooth.
Add the wet ingredients to the oat and yogurt mixture and stir until combined.
In another bowl, sift together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, folding gently until just combined. Do not overmix.
Divide the batter evenly among the prepared muffin cups, filling each about 3/4 full.
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.