Heat the oven to 175 °C and line a loaf pan with parchment.
Melt the butter in a light-coloured pan over medium heat and cook, swirling, until the solids turn deep golden and smell nutty, about 5 minutes. Cool slightly.
Mash the bananas, then whisk in the eggs, brown sugar, vanilla and brown butter.
Fold in the flour, baking soda, salt and cinnamon until just combined.
Scrape into the pan, sprinkle generously with demerara, and bake until a skewer comes out clean, about 55 minutes.
1 h 15
