4 oz. very thinly sliced country ham or prosciutto

1 cup coarse fresh breadcrumbs

4 tablespoons olive oil, divided

1 teaspoon chopped fresh thyme

1 cup finely grated Parmesan, divided

Kosher salt and freshly ground black pepper

2 bunches collard greens (about 1 lb.), center ribs and stems removed

1 large onion, thinly sliced

2 garlic cloves, finely chopped

2 tablespoons unsalted butter

2 tablespoons all-purpose flour

2 cups whole milk

¼ teaspoon freshly grated nutmeg

Pre-reheat oven to 325°. Place ham on a parchment-lined baking sheet and bake until crisp, 20–25 minutes; let cool and break into pieces.  Combine breadcrumbs and 2 Tbsp. oil in a medium skillet; toast over medium heat, tossing occasionally, until golden brown and crisp, 10–15 minutes. Remove from heat and add thyme and ¼ cup Parmesan; season with salt and pepper. Mix in ham and set aside.  Cook collard greens in a large pot of boiling salted water until tender and bright green, about 4 minutes. Drain, transfer to a bowl of ice water, and let cool. Drain and squeeze dry with paper towels. Coarsely chop greens and place in a large bowl.  Heat remaining 2 Tbsp. oil in a medium saucepan over medium heat. Add onion and garlic and cook, stirring often, until softened and golden, 15–20 minutes. Transfer to bowl with greens; set aside. Reserve saucepan.  Increase oven temperature to 400°. Melt butter in reserved saucepan over medium heat. Add flour and cook, whisking constantly, until mixture is smooth and very pale brown, about 4 minutes. Gradually whisk in milk, ½-cupful at a time; add nutmeg. Bring to a boil, reduce heat, and simmer, whisking often, until thickened, 5–8 minutes. Whisk in remaining ¾ cup Parmesan. Add béchamel to collard green mixture and mix to combine; season with salt and pepper.  Transfer collard green mixture to a 10” cast-iron skillet or 9” pie dish and top with breadcrumb mixture; place pie dish on a rimmed baking sheet. Bake until gratin is bubbling, 15–20 minutes. Let cool slightly before serving.