Wash the rhubarb stalks thoroughly, trim off the ends, and slice the stalks into pieces about 1/2 inch thick. Discard all rhubarb leaves because they are not used in this recipe.

Place the sliced rhubarb, granulated sugar, and water in a medium saucepan. Stir briefly so the sugar is moistened and the ingredients are evenly distributed.

Bring the mixture to a boil over medium to medium-high heat, stirring occasionally. Once bubbling, watch the pan closely as the rhubarb begins releasing its juices.

Reduce the heat and simmer uncovered for about 10 minutes, or until the rhubarb is very tender and the sauce has thickened slightly. Stir from time to time to prevent sticking and to help the fruit cook evenly.

Remove the saucepan from the heat and stir in the vanilla extract. Taste only after the sauce has cooled slightly, then serve warm or transfer it to a container to cool and refrigerate.