Prepare the Rhubarb Compote: In a medium saucepan, combine chopped fresh rhubarb, 1/4 cup sugar, lemon juice, and a splash of water. Heat over medium heat, stirring occasionally until it simmers. Cook for about 15 minutes until the rhubarb softens and thickens. Cool and puree until smooth.

Whisk the Egg Mixture: In a mixing bowl, whisk together egg yolks, one whole egg, and 2/3 cup sugar until light and frothy, about 3-4 minutes. Set aside.

Heat the Heavy Cream: In another saucepan, heat 2 cups of heavy cream over medium heat until steaming. Gradually whisk a small amount into the egg mixture.

Combine and Cook the Mixture: Return the mixture to the saucepan and stir over low heat for 5-7 minutes until it thickens. Strain through a fine mesh sieve.

Chill the Mixture: Allow the custard to cool at room temperature for 30 minutes, then refrigerate for at least 2 hours.

Combine Compote and Custard: Once cooled, combine the compote and custard in a mixing bowl and fold together until smooth.

Churn the Ice Cream: Transfer to an ice cream maker and churn according to instructions for 20-25 minutes.

Freeze the Ice Cream: Transfer to an airtight container, smooth the top, cover, and freeze for about 4 hours until set.