Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, combine the rolled oats and Greek yogurt. Stir well and let the mixture sit for 5 minutes to soften the oats.
Add the granulated sugar, eggs, vegetable oil, and vanilla extract to the oat and yogurt mixture. Whisk until smooth and well combined.
In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt.
Gradually add the dry ingredients to the wet ingredients, stirring 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 pan for 5 minutes before transferring them to a wire rack to cool completely.