Put the broccoli in a pan of water. Bring to the boil, then remove the rosettes with a slotted spoon into cold water. Keep the hot water.
Drain the broccoli and put it in a food processor. Add all other ingredients and pulse until you get a textured paste - you might need to add a drop of the cooking water. Taste and adjust the seasoning, herbs etc to your liking. Set aside.
Reheat the pan of water. When boiling, add the gnocchi and cook them until they float to the surface.
Remove them with the slotted spoon into a mixing bowl.
Add the pesto and combine well.
Serve with grated cheese, garnished with mint leaves.