Preheat the oven to 375 degrees F. Line a 12-cup muffin tin with paper muffin liners.
Peel the bananas and add to a large bowl. Add the agave syrup and mash the bananas with a fork until very liquefied but still a little lumpy.
Melt the butter in a small saucepan or skillet over medium heat. Cook, stirring occasionally, until the milk solids have turned a nutty golden brown.
To the brown butter, add about 1 cup of the mashed banana mixture and whisk to combine. Cook for a few more minutes until a darker golden color is achieved. Add to the remaining mashed banana mixture and whisk to combine, then whisk in the egg. Fold in the flour, in 2 batches, with a rubber spatula, until just combined; do not over mix. With an ice cream scoop, evenly divide the batter among the muffin tin cups.
Bake in the center of the oven until golden brown and the tops spring back when pressed, about 25 minutes. Cool for 5 minutes in the pan, then transfer the muffins to a rack to cool completely. Serve warm or at room temperature.