Wash and cut up the tarragon leaves with scissors. “Massage” the tarragon into the butter – I used my fingers to do it, though a fork would do as well.
Place a walnut of tarragon butter inside the game hens. Rub the rest of the tarragon butter all over them.
Put some olive oil in a Dutch oven, and brown the game hens on all sides, until golden.
Add ¼ cup of water to the bottom of the Dutch oven, cover and cook for about 40 minutes, until the meat is done. Remove the game hens and set aside.
The sauce: Put some ice cubs in a strainer, over a pan or bowl. Pour the cooking juices over the ice (this is to take out the excess grease, which should stick to the ice). Pour the cooking juices back into the Dutch oven, scraping the bits at the bottom. Over low heat, whisk in the egg yolk and the cream, with some fresh cut up tarragon, for 2-3 minutes max.
*A note on the sauce: It is there to complement the delicate flavor of the meat, it should definitely not “drench” the meat. I gave very little of it to my son, just to taste.
You can serve this, for example, with a creamy polenta, or as above, a baby bok choy puree.
Age: This is a dish for the whole family, but you can start at 8-12 months. Depending on your child’s motor skills, give meat as finger food or puree it, or for an older toddler, hand him/her the drumstick as above!