To make the syrup, combine sliced rhubarb and water in a small pot.
Bring to a boil and cook until the rhubarb falls apart, about 5-10 minutes.
Strain the liquid through a fine sieve and pour back into the (cleaned!) pot. (Discard the rhubarb pulp left in the sieve.)
Add sugar, lemon juice, and vanilla.
Boil for 10 minutes and make sure the mixture doesn't boil over.
Let cool and pour into a sterilized jar. (Store leftovers in the fridge for up to two weeks.)
To make the compote, combine rhubarb and sugar in a small pot and bring to a boil.
Cook until the rhubarb falls apart.
Set aside and let cool completely.
To make the ice cream, combine coconut milk, oil, and sugar in a bowl and whisk. Add syrup and whisk again.
Transfer to a shallow container such as a brownie pan and place in the freezer.
Freeze for 2-3 hours, or until mostly solid.
Once the coconut milk mixture is frozen, combine the chickpea brine and the remaining sugar.
Whip the mixture with a hand held mixer or in a stand mixer until very stiff. This may take up to 10 minutes. You can add a splash of lemon juice to speed up the process.
Cut the frozen coconut milk mixture into smaller pieces and transfer to a high speed blender.
Blend until it has the consistency of soft serve.
Pour into the chickpea fluff and fold the fluff into the coconut mixture until everything is smooth. Make sure to do this slowly and carefully. You don't want the chickpea foam to collapse too much.
Pour into a container and freeze for another 2-3 hours.
Fold in the rhubarb compote and freeze until solid.