Preheat your oven to 375°F (190°C). Grease a muffin tin or line with paper liners.
In a large bowl, combine the oats and milk. Let sit for 10 minutes.
In another bowl, whisk together the flour, brown sugar, baking powder, baking soda, and salt.
Add the egg, oil, and vanilla to the oat mixture. Stir to combine.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
Divide the batter evenly among the muffin cups.
Bake for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.