1. In a medium saucepan over medium heat, bring rhubarb and water to a simmer. Cook, stirring occasionally, for 15 minutes or until rhubarb is soft and mixture resembles thick applesauce. Using the back of a wooden spoon, push through a fine sieve. Set aside.
2. In a bowl, whisk eggs with sugar until thickened and pale yellow. Set aside.
3. In a separate medium saucepan over medium-low heat, bring milk and cream to a simmer. Gradually whisk into the egg mixture.
4. Return entire mixture to the saucepan. Cook over low heat, stirring constantly, until the mixture is thick enough to coat the back of a wooden spoon. Be careful not to let it boil. Strain into a clean large bowl. Let cool to room temperature.
5. Stir in rhubarb mixture and strawberries. Cover and refrigerate until completely cold or overnight.
6. Stir cream mixture. Transfer to an ice cream maker and freeze according to manufacturer's instructions.