Preheat oven to 350ºF.

Use a sharp knife to cut each squash from stem to bottom. Scoop out the pulp and seeds and discard them. Rub salt and pepper on the inside of the squash.

Over medium heat, melt the butter in a large skillet. Add the shallots and cook them for about 5 minutes, or until softened. Stir in the mushrooms and garlic and cook about 5 minutes more, or until the mushrooms have released their juices and are nicely browned. Fold in the kale and continue to cook until it wilts, about 3 minutes more. Remove from heat and season with salt and pepper to taste.

Transfer the vegetable mixture to a large bowl. Add the bread, cheese, nutmeg, and cream and stir until combined. Divide the filling into the squash halves. Place the squash on a rimmed baking sheet or baking dish lined with foil, then cover the entire baking sheet with a large piece of foil.

Bake the squash for 30 minutes, then remove the foil and bake for 30-40 minutes more, or until the filling is browned and crispy on top and the squash is easily pierced with a knife.

Remove the squash from the oven and allow them to set for 10 minutes before serving.