Preheat the oven to 350 degrees F. Grease a mini muffin pan very well with butter. Do not use liners. You want the crispy exterior.
In a small bowl, prepare the flax egg by combining the ground flaxseed and water. Stir and set aside for 5 minutes to thicken.
In a large bowl, whisk together the flour, dark brown sugar, baking powder, and salt. In a smaller bowl, add the flax egg, melted butter, coconut milk, and vanilla. Whisk until well combined. Add wet to dry and whisk until well combined.
Scoop batter into mini muffin tins. Fill it all the way to the top. Sprinkle tops with sesame seeds. Bake for 30-35 minutes until golden brown. Cool in the pan for 5-10 minutes. Remove and place on a wire rack to cool completely. Store in an airtight container on the counter for 3 days. You can pop them in the microwave for 5-10 seconds to reheat them. Enjoy!