Heat 1 tablespoon of olive oil in a large oven-proof dutch oven over medium high heat. Season the lamb pieces with salt and pepper then, working in batches, add them to the pot and brown them on all sides. Transfer the lamb to a plate.
Add the remaining tablespoon of olive oil to the pot, then add the onion, garlic, and mushrooms along with a pinch of sea salt. Cook until the onion is tender, about 6-7 minutes.
Stir in the tomato paste and cook until it starts to brown, 2-3 minutes.
Pour in 1 cup of the beef stock and deglaze the bottom of the pot, scraping up all the browned bits with a spoon.
Add the lamb along with any accumulated juices back to the pot. Pour in the remaining 2 cups of stock, balsamic vinegar, and fish sauce. Add the roasted red peppers and fresh thyme to the pot, and season with more sea salt and pepper to taste.
Bring the pot to a low simmer, then cover it and transfer it to the oven. Cook for about 2 hours, or until the lamb is extremely tender.
Add the butternut squash to the pot, then continue to cook for another 20-30 minutes until the squash is tender.
Remove the pot from the oven and return it to a burner over medium heat. Dissolve the arrowroot powder in the water, then pour it into the pot. Simmer for 5 minutes, stirring occasionally, until thickened.
Season the stew with more sea salt and pepper to taste and garnish with fresh parsley before serving.