Pat the diced lamb dry with paper towels so it browns nicely.
In a bowl, toss the lamb with the gluten-free flour and a good pinch of salt and black pepper until evenly coated.
Chop the onion, slice the carrots and celery, mince the garlic, halve the baby potatoes, and slice the mushrooms if using.
Heat the olive oil in a large Dutch oven or heavy pot over medium-high heat
Add the lamb in batches (do not overcrowd the pan) and sear until browned on all sides, about 5-7 minutes per batch.
Transfer browned lamb to a plate and repeat with the remaining pieces, adding a little extra oil if needed.
Reduce the heat to medium. In the same pot, add the onion, carrots, and celery.
Cook, stirring often, until they begin to soften, about 5 minutes. Stir in the garlic and mushrooms (if using) and cook for 1-2 minutes more, just until fragrant. Add the tomato paste and cook, stirring constantly, for another minute to caramelize it slightly.
Pour in the red wine (or extra broth) and scrape up any browned bits from the bottom of the pot with a wooden spoon. Let it simmer for 2-3 minutes to reduce slightly.
Return the browned lamb (and any juices) to the pot. Add the baby potatoes, gluten-free beef or lamb broth, rosemary, thyme, and bay leaves. Stir to combine.
Bring the stew up to a gentle boil, then reduce the heat to low, cover with a lid, and let it simmer for about 1½ to 2 hours, or until the lamb is very tender and the flavors have melded. Stir occasionally and check that it’s only gently bubbling.
Once the lamb is tender, taste the stew and adjust with more salt and black pepper if needed. If you’d like it thicker, simmer uncovered for 10-15 minutes.
Remove the bay leaves and discard. Stir in the chopped fresh parsley right before serving. Serve hot with gluten-free bread, mashed potatoes, or over rice.