Preheat the oven to 360°F. Line a 12-cup muffin pan with paper liners.

Beat the butter and sugar together until pale and fluffy. Add the eggs and beat in for 1 minute, then mix in vanilla extract and milk. Add the gluten-free flour to the bowl with all the wet ingredients and mix well. Finally, fold in the blueberries, raspberries, and strawberries, and divide the mixture between the muffin cups. Sprinkle with oats.

Bake for 12 minutes or until a toothpick inserted into the center comes out clean. Remove from the oven, let cool, and serve.