Place the half-and-half and the heavy cream into saucepan, and heat over medium heat. Bring the mixture just to a simmer, stirring occasionally and remove from heat.
In mixing bowl whisk the egg yolks until they lighten in colour, then gradually whisk in the sugar. Temper the egg mixture by gradually adding small amounts of the cream, until ⅓ has been added. Pour in the remainder and return the entire mixture to the saucepan. Continue to cook over low heat, stirring frequently, until the mixture thickens slightly and coats the back of a spoon -reaching 170 to 175 degrees F.
Pour the ice cream base mixture into a container and cool at room temperature half an hour. Stir in the vanilla, and the inside scraping of the vanilla bean (or omit the vanilla bean and use 2 teaspoon of vanilla extract). Refrigerate the mixture 4-8 hours until the temperature is 40 degrees F or below.
To make the rhubarb compote, stir the rhubarb pieces and ⅓ cup sugar in a medium saucepan, and let sand off the heat about 10 minutes, until the rhubarb releases some of its liquid. Next bring the rhubarb mixture to a boil over medium-high heat, stirring occasionally. Reduce heat to medium and let simmer, stirring occasionally until the rhubarb pieces have broken down, about 5 minutes. Remove from heat, and let the cooked fruit cool. Set aside.
For The Strawberry mixture, combine strawberries, ⅓ cup sugar, pinch of salt, and 2 tablespoon of water in a small saucepan. Bring to a simmer over medium heat. Cook stirring occasionally until the strawberries begin to break down, and the juices thicken -about 15 minutes. Remove from the heat, and add vanilla and lemon juice. Let cool, and set aside.
Pour the cooled ice cream mixture into your ice cream maker and follow the manufacturer’s direction to churn ice cream. When the ice cream is a soft serve consistency stir in ribbons of the cooled rhubarb and strawberry fruit mixture to taste. Place in an airtight container and freeze 3-5 hours before serving