In a large stockpot, heat the oil over medium. Add onion, season with salt and pepper. Cook, stirring frequently, for about 5 minutes, until softened. Slowly add 1/3 cup of the cider. Continue to add remaining cider to caramelize the onions, about 10 minutes. Add apples, squash, thyme, and cook over medium heat, stirring until softened, 8 minutes. Add beer, 3 cups of broth, and the cayenne. Increase heat to high, bring to a simmer, and cook for 15 to 20 minutes, or until apples and squash are tender.