Preheat the oven to 325°F, and season the roast with 1 teaspoon of salt. Place the ghee (or olive oil) in a heavy-bottomed or enameled cast iron pot over high heat. Once hot, sear the roast on one side for 4 minutes, then flip it over and remove the pot from the heat. Pour the broth into the pot until it reaches halfway up the roast, then place the lid on the pot, and bake for 3 hours.
While the roast is in the oven, place the squash halves cut side down on a baking sheet or in a casserole dish, and bake for 1 hour and 15 minutes (at the same time as the roast).
While the roast and acorn squash are in the oven, caramelize the onions. Add the butter to a heavy-bottomed pot over low heat, and once melted, add the sliced onions and 1 teaspoon of salt. Stir to combine, then place a lid on top, and let the onions wilt for 30 minutes. After 30 minutes, take the lid off the skillet and toss the onions in the butter. Turn the heat up to medium-low, and let the onions continue to caramelize, uncovered, for 45 minutes, scraping the pan and stirring the onions occasionally.
Once the roast is finished, use two forks to shred it. Then, put the shredded beef, caramelized onions, cranberries, the final teaspoon of salt, and pepper in a large bowl and toss to combine. Stuff equal portions of the beef mixture into the squash halves. Raise the oven temperature to 375°F.
If the acorn squash is still warm when you stuff it, bake for 10 minutes, until the beef is slightly browned the and stuffing is fully warmed through. If the acorn squash is cool when you stuff it, tent the stuffed squash with aluminum foil, and bake it for 25 minutes, until both the squash and stuffing are warmed through.
While the stuffed squash is in the oven, make the sauce by whisking or blending together the Greek yogurt, lemon juice, grated garlic, salt, and thyme.
Pour the sauce over the stuffed squash, sprinkle with fresh thyme leaves, if using, and serve!