In a large saucepan, heat 1 tablespoon of the oil over medium heat. Add the onion and sauté until translucent, about 5 minutes. Transfer the onion to a plate, leaving the oil in the pan.
Brown the meat in the reserved oil over medium-high heat, stirring to break it up into even crumbles. Return the onion to the pan. Add the water, tomato paste, vinegar, garlic, salt and pepper. Tie the pickling spice and cinnamon in a small piece of cheesecloth and add to the stew.
Reduce the heat to low, cover, and simmer for 1 hour, stirring occasionally and adding additional water if it threatens to scorch. Discard the cheesecloth.
PREPARE THE REST:
Preheat oven to 350°F. Line a baking sheet with parchment paper.
Cut the squash in half lengthwise and scoop out the seeds. Place the squash, cut-side-down, on the prepared pan. Bake until the flesh can be easily scraped into strands with a fork, about 50 to 70 minutes. Remove from the oven and let cool slightly. Using a fork, scoop out all the flesh into a bowl and fluff the spaghetti-like strands. Toss in the salt and pepper. Place on a large, warmed platter or the cleaned squash shell.
Melt the butter in a small saucepan over medium heat and cook until it turns light brown. Pour over the squash strands. Toss with the fork to blend.
Top the squash with the hot meat sauce. Scatter the avocado and tomatoes and tomatoes over and sprinkle with the cheese and parsley. Serve immediately.