Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, combine the rolled oats, Greek yogurt, and whole milk. Stir well and let the mixture sit for 10 minutes to soften the oats.
In a large bowl, whisk together the eggs, granulated sugar, vegetable oil, and vanilla extract until smooth.
In a separate bowl, sift together the all-purpose flour, baking powder, baking soda, and salt.
Add the oat and yogurt mixture to the wet ingredients and stir to combine.
Gradually fold the dry ingredients into the wet ingredients, mixing gently until just combined. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
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 allow them to cool in the tin for 5 minutes before transferring to a wire rack to cool completely.