In a medium Dutch oven, combine collard greens, 3 cups water, vinegar, and 1 teaspoon salt; bring to a boil over medium-high heat. Reduce heat to medium-low; cook until tender, about 25 minutes. Drain.
Preheat oven to 350°.
On a small, rimmed baking sheet, place cornbread crumbs. Bake until lightly toasted, 6 to 8 minutes.
In a 10-inch cast-iron skillet, melt 3 tablespoons butter over medium heat; add mushrooms, onion, and garlic. Cook, stirring occasionally, until softened, about 7 minutes. Sprinkle flour over mushroom mixture; cook, stirring constantly, for 1 minute. Gradually whisk in milk. Bring mixture to a gentle boil over medium-high heat, stirring constantly. Reduce heat to medium-low. Cook, stirring constantly, until thickened, about 3 minutes. Remove from heat. Stir in collards, cheese, and remaining 1 teaspoon salt.
In a medium bowl, toss together cornbread crumbs and 2 tablespoons melted butter. Sprinkle over collard mixture. Bake until bubbly, about 25 minutes.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/collard-greens-casserole/