Preheat the oven to 140 degrees Celsius (284 degrees Fahrenheit) (conventional oven).
Get a large roasting pan.
Trim the excess fat from the lamb and place it in the roasting pan.
Peel your garlic and slice it thinly.
Slice your limes thinly.
Score the surface of the lamb and place a slice of garlic over the cuts.
Season with salt and pepper.
Add the fresh thyme on top and cover the lamb with lime slices.
Peel the onions, carrots, and leeks and cut them into smaller pieces.
Place the lamb in the roasting pan and add all the vegetables and wine/water.
Put it in the oven with a meat thermometer. The thermometer should be right next to the bone, and we're aiming for a final temperature of 63 degrees Celsius (145 degrees Fahrenheit).
Cook the lamb for 2.5 hours at 140 degrees and then take it out of the oven.
Reduce the oven temperature to 110 degrees.
Remove the cooking juices and pour them into a jug/tall bowl. Chill the bowl, and when the oven reaches 110 degrees, put the lamb back in the oven.
When the meat reaches 63 degrees, take it out. It took me about 1 hour.
Take the meat out of the oven and let it rest for 15 minutes.
If you have access to a blowtorch, you can give it a quick sear on top before slicing the meat. It has been cooked at a low temperature, so this can give it a bit of a crust.
Slice the meat thinly and serve with flake salt.
Here, the sauce is made from the drippings of the lamb. The reason I let it cool a bit first is that the fat settles on top of the drippings, making it easy to remove.
I went all in on the lamb flavor and used the fat instead of butter for my roux-based sauce. Of course, you can "just" use butter or oil.
Melt the fat over medium-high heat in a saucepan/small pot. I used 9 out of 14 on my stove.
Once melted, add the flour and whisk it hard to distribute it well. Let it simmer for 2-3 minutes to cook the flour taste out of the sauce.
First, add milk while whisking vigorously to avoid lumps. Then add the drippings (use stock/broth if you don't have any), and let it simmer for a couple of minutes, stirring regularly.
Now add the cream and browning.
Let it simmer for a couple more minutes and then season the sauce to taste:
Start with salt and pepper, a bit of sweetness (sugar/red currant jelly), a little vinegar, and lemon juice. Use more of these ingredients if you feel something is missing.
Let it simmer for a couple more minutes, and the sauce is ready.
Enjoy.
