Melt the butter in a Dutch oven over medium heat. Continue cooking it until it turns golden brown and smells nutty, about 3 minutes.
Add the lamb cubes to the brown butter. Brown them on all sides for 6 to 8 minutes, seasoning with salt and pepper as they cook.
Stir in the diced onion and sliced carrots. Cook for 5 minutes until the onion softens.
Add the quartered mushrooms and thyme sprigs. Cook for another 3 minutes to release the mushroom liquid.
Pour in the broth and add the cubed potatoes. Bring the mixture to a boil, then reduce to a simmer.
Cover and cook for 1 hour 15 minutes, stirring occasionally, until the lamb is tender and the potatoes are soft. Remove the thyme stems before serving.