Oil a 9- by 5-inch loaf pan with cooking spray and line the bottom and up the sides with a 9- by 15- inch sheet of parchment paper. Oil parchment with cooking spray. Heat the oven to 350 degrees. If you haven’t cooked the quinoa, do it now.
Heat oil in a large (12-inch) skillet over medium-high heat; add squash, onion, celery, garlic, chestnuts, and the rosemary; sautéing for a few minutes to start the cooking process and seasoning with salt and pepper. Reduce heat to medium low, add the cayenne, paprika, and oregano and continue to cook until vegetables are fully cooked, about 15 minutes, stirring in the mushrooms the last 5 minutes of the cooking process. Remove from heat, stir in butter and lemon zest, and transfer to a large bowl. Add quinoa, breadcrumbs, cranberries, apricots, and nuts; toss to combine. Adjust seasonings to taste, including salt and pepper. Add eggs; toss to combine. Turn into prepared pan and bake until golden and set, about 45 minutes.
Meanwhile, heat cinnamon sticks, pepper flakes, and oil in a large skillet over medium-high heat until pepper flakes start to sizzle. Add onions, garlic, and thyme; sauté until tender, about 5 minutes. Add tomatoes and about a half can of water and bring to a simmer. Reduce heat to medium-low and continue to simmer to blend flavors and reduce to sauce consistency, about 20 minutes. Remove cinnamon sticks from sauce.
Remove roast from oven, loosen at each end, turn onto a work surface, and then transfer to skillet of tomato sauce. Sprinkle with cheese and garnish with cinnamon sticks and thyme. Return to oven and continue to cook until cheese melts and sauce is simmering, 10 to 15 minutes longer. Remove from oven, transfer roast to cutting board and let rest to firm up,10-15 minutes. Keep sauce warm, adding water as necessary to create a juicy, spoonable sauce. Slice, serving with a portion of sauce.