For the Strawberry Compote: Combine strawberries and sugar with 3 tablespoons water over medium-low heat. Cook, partially covered, until berries release some juice but remain whole, 5 to 10 minutes. Let cool.
For the Rhubarb Compote: Heat oven to 450 F. Place rhubarb and sugar in an ovenproof casserole; toss to coat. Cook until rhubarb is soft, but keeps shape, 25 to 40 minutes. Let cool, then stir in cream.