Zucchini Mushroom Pasta

1 spaghetti squash, halved lengthwise and seeded;

1 pound cremini mushrooms, sliced;

2 zucchini, chopped;

2 shallots, sliced thinly;

2 cloves garlic, minced;

2 sprigs thyme;

¼ cup coconut milk;

3 tbsp. olive oil;

Cooking fat;

Sea salt and freshly ground black pepper;