Preheat the oven to 350°F (175°C). Lightly grease or line 6 mini muffin cups.
In a bowl, combine milk and oats. Let sit for 5 minutes to soften.
While oats soak, mix softened butter, honey, and cinnamon in a small bowl until smooth. Set aside.
Add melted butter, brown sugar, egg, and vanilla to the oat-milk mixture. Stir to combine.
Add flour, baking powder, baking soda, and salt. Stir just until combined, then fold in blueberries.
Divide batter evenly among muffin cups. Bake 12–15 minutes, until tops are golden and a toothpick comes out clean. Cool slightly.
While muffins bake or cool, portion fruit onto plates and pour milk into glasses.
Serve muffins warm with cinnamon honey butter dip on the side, along with fruit and milk.