Halve the squash lengthwise and scoop out the seeds with a spoon. Set the squash halves cut-side-up in a baking dish. Drizzle them with olive oil and sprinkle with sea salt. Bake until fork tender, 35 to 40 minutes. Remove from the oven and use a fork to separate the flesh into strands. Transfer the squash "noodles" to a medium mixing bowl. Set aside.
Heat 1 tablespoon of the olive oil in large skillet over medium-low heat. Add the garlic and cook until lightly browned, 2 to 3 minutes. Add the broccoli and cook another 8 minutes, or until tender. Stir in the oyster mushrooms, rosemary, thyme and red pepper flakes, and cook 3 minutes more. Add the cherry tomatoes and green olives, and cook for a final 2 minutes. Transfer the mixture to the bowl with the spaghetti squash. Add the remaining 1 tablespoon olive oil and toss to combine. Season with salt and pepper. Garnish with the pine nuts and serve immediately.