Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
In a bowl, combine the oats and milk. Let them soak for about 10 minutes.
In another bowl, whisk together the flour, brown sugar, baking powder, baking soda, and salt.
Add the egg, oil, and vanilla extract to the oat mixture. Mix well.
Combine the wet and dry ingredients, stirring until just combined. Do not overmix.
Fill the muffin cups about ⅔ full with the batter.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for a few minutes, then transfer to a wire rack to cool completely.