For the acorn squash: Preheat the oven to 375 degrees F. Trim the tops and bottoms off the squash. Cut in half horizontally so the cut-ends will keep the pieces flat. Clean the inside of the squash. Separate the seeds from the membranes and rinse well. Dry the seeds with a paper towel and set aside.
Place the squash cut-side up on a baking sheet, drizzle with the olive oil and sprinkle with 1 teaspoon of the salt and the pepper. Place the seeds on a separate baking sheet or foil. Roast the squash 30 minutes. Roast the seeds at the same time, checking and moving them around after 10 minutes and again after 20 minutes. Depending on the size of the seeds, they may be done after 20 minutes, or up to 30 minutes. Sprinkle the seeds with the remaining salt, and set aside with the squash.
For the filling: Set a large saute pan over high heat and add the butter. When melted, add the cabbage, onions, peppers, sprinkle with salt and pepper and gently toss to combine. Allow the cabbage to wilt down, about 5 minutes. Add the mushrooms and cook, 3 to 4 minutes. Add the garlic and toss to combine. Saute 2 to 4 minutes longer, and adjust the seasoning with salt and pepper.
For assembling: Preheat the broiler to low. Fill the roasted acorn squash halves with the filling. Sprinkle the crumbled goat cheese over the top, then top with the roasted squash seeds. Broil just until the cheese is warm. Garnish with a small amount of Italian parsley, if using, and serve.