Pre-heat oven to 375˚F and place a ripe banana in a rimmed baking sheet with skin on. When oven is to temperature, roast banana in oven for 15 minutes.
Remove banana and let cool to the touch. Skin the banana, making sure to reserve all the juices. Roughly cut the banana into about 8 large pieces and dump the pieces and the juice into a blender or food processor.
Pulse the banana and juice until it's a thick paste. Add the stone-ground mustard and pulse again, mixing thoroughly. Slowly drizzle in the olive oil until the mustard is smoothly blended. Set aside until ready to use.