Prepare rhubarb: Clean and chop into small pieces, about 3 cm/ 1.2 inch. Place in a pot and add the water and 100 g/ 3.5 oz/ ½ cup sugar. Cover, bring to a boil, and simmer on low heat for about 5 minutes. Strain through a sieve, but don't push through the strainer.
Preheat the oven to 160 degrees Celsius/ 320 degrees Fahrenheit.
Make the custard: Beat the eggs, egg yolks, sugar, and vanilla extract with a fork. Bring the milk to a boil, but don't let it boil (Note). Slowly add the milk to the egg mixture while beating with the fork. Add the rhubarb and stir gently. Pour everything into a baking dish.
Waterbath: Place the baking dish with the custard into a larger baking tray and pour boiling water (from a kettle) into the larger tray to come halfway up the baking dish containing the custard.
Bake for 45 minutes to 1 hour. It is done when the top of the custard is quivering to the touch, but it is not liquid. Take the custard out of the water and let it stand for a while before serving; it will continue setting while it stands.
Notes
Heat the milk in a heat-proof jug; it will be easier to pour it into the egg mixture. Or heat it in a saucepan and transfer it to a jug for easy pouring.