Preheat the oven to 350°F (175°C).
In a large pot, bring water to a boil and cook the cubed butternut squash until tender, about 10-12 minutes.
Drain the squash and return it to the pot. Mash it until smooth.
In a skillet, sauté the chopped onion and minced garlic in a bit of olive oil until soft and translucent.
Add the sautéed onion and garlic to the mashed squash, along with heavy cream, thyme, nutmeg, salt, and pepper. Mix well.
Fold in the grated cheddar cheese until evenly distributed.
Transfer the mixture to a greased baking dish and smooth the top.
Sprinkle the breadcrumbs evenly over the top of the casserole.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown.
Let the casserole cool for a few minutes before serving.