Preheat the oven to 375˚F, and generously butter a baking dish. I used a pie plate for mine.
In a large frying pan, melt the butter over medium-high heat. Add the mushrooms and shallots and cook until the shallots are soft and the mushroom begin to melt into the butter, about 7 minutes.
Add the butternut squash and sauté until it softens and begins to brown, about 15 minutes. After the squash has been sautéing for 10 minutes, add the ginger and apple slices. Sauté all together for the final 5 minutes. Add a little extra butter if the skillet is dry, but no more than 1/2 tablespoon.
Stir in the broth, thyme, dried cherries, and salt.
Pour the squash filling into the prepared baking dish. Cover with foil and bake until just tender, about 20 minutes.
Combine all the Crumble ingredients together in a small bowl except the butter. Chop the butter into pieces and add to the mixture. Pinch the butter in the mixture until the crumble is coarse, and some chunks of butter are the size of peas. This can also be done in a small bowl of a food processor fitted with a blade. Just pulse until the chunks of butter are no larger than a pea.
When the squash filling comes out of the oven, scatter the crumble over the top and return to the oven for another 20 minutes, or until the topping is golden brown.