Add rhubarb to a medium saucepan and add 1/2 cup water. Cover and cook, stirring occasionally, over low heat until rhubarb is completely broken down and reduced to a thick paste, about 45 minutes.
Add 1 cup of sugar, cook, stirring frequently until the sugar has dissolved, and remove from the heat. Chill in the refrigerator until cool.
In a mixing bowl, whisk 1 1/2 cups Greek yogurt, the rhubarb paste (you should have about 1 cup) and the second cup of sugar until fully incorporated. Spin the mixture in your ice cream machine according to manufacturer's instructions.