Heat oven to 350º F with a rack near the middle.

Combine winter squash, half-and-half, and eggs in a small bowl or large glass measure. Set aside. Combine cornmeal, 1 teaspoon salt, baking powder, black pepper, aleppo or cayenne pepper, and Gruyère in a large bowl. Set aside.

Heat half of the butter in a 10-inch cast iron skillet over medium heat. Once the foaming has subsided, add the leek slices and ⅛ teaspoon salt. Cook until soft and just starting to brown, stirring occasionally. Add the thyme and cook until fragrant, 30 to 60 seconds. When leeks are almost done, add the squash mixture to the cornmeal mixture. Scrape the leeks into the squash and cornmeal mixture (it's okay if there are a few stragglers left in the pan).

Add remaining butter to the skillet and return the skillet to medium-low heat.

Stir together the leek, squash, and cormeal mixture until combined. Fold in the bread cubes, and adjust salt to taste. Pour into the skillet. Transfer skillet to oven and bake until puffed and golden brown, about 45 minutes. Cool 10 minutes before serving.