Mix butter, brown sugar, and honey together in a bowl. Spoon about 1/6 of the butter mixture into the cavities of each of the butternut squash halves and the acorn squash halves. Arrange squash halves in large baking dishes.
Roast squash in preheated oven for about 30 minutes. Arrange apples around the squash halves and continue baking until flesh is easily removable with a spoon, about 30 minutes more.
When you add the apples to the oven, heat olive oil in a small skillet over medium-low heat; add onion and thyme. Cook onion, stirring frequently, until completely caramelized, about 30 minutes.
Scoop roasted squash into a large pot; add apples and caramelized onion. Pour vegetable stock, apple cider, and water into the pot; bring to a boil and remove from heat.
Pour soup into a blender no more than half full. Cover and hold lid down; pulse a few times before leaving on to blend. Puree in batches until smooth. Reheat before serving, as needed.