Combine the rhubarb and half the sugar in a small saucepan with 1 Tablespoon of water over medium-high heat, and let it soften to a fall-apart paste. Add more water as needed until it's super soft but not runny, then add it to a blender.
Place the egg yolks, unbroken, into a large bowl. It's okay if they break, but try to avoid it!
Combine the remaining heavy cream, the milk, salt, and the rest of the sugar in a small saucepan over medium heat. Heat until it's starting to steam, mixing in the sugar until dissolved.
Strain the hot milk mixture into a separate bowl. Using a teaspoon measure, add the hot milk into the egg yolks a teaspoon at a time, then once most of it is added, mix the yolks in until the mixture is creamy and golden yellow.
Pour the mixture back into the saucepan, and add in the vanilla. Continue cooking over medium-low heat until the mixture coats the back of a spoon, no more than 160°F. You want to be very careful to constantly mix it so there's no chance of it getting chunky!
Remove the custard from the heat once thickened, and pour it through a fine-mesh strainer into the blender with the rhubarb compote. Blend until well-mixed! You can add a drop of red food coloring for extra pink color if you want.
Place the mixture in a bowl (or keep it in the blender!) and cover it with plastic wrap, then place it in the fridge. Let it chill until it's completely cool, 4-8 hours. It won't churn at all if it's not cold! If it's still too hot to put in the fridge, quick-chill it in an ice bath.
Once the custard mix has chilled, pour it into the basin of your ice cream maker and churn according to your mixer's instructions. Then scrape it into a pint-sized loaf pan, and enjoy!