Soak the tapioca in water to cover, refrigerate and overnight. Drain the next day. Place all the ingredients in a saucepan and simmer 20 minutes until tender. Chill (it will thicken as it chills).
To make the tarragon syrup, blanch the tarragon leaves and spinach in boiling water for 10 seconds then shock in ice water. Squeeze out the water and chop coarsely. Add simple syrup and oil then puree with hand blender for 3 minutes. Pass it through a fine chinois. Chill.
To serve, spoon the tapioca into a shallow bowl, surround it with a ring of tarragon syrup and tuck in banana slices around the edge.