Preheat the oven to 375 degrees F and butter a 4-quart casserole dish.

Chop the bacon into small pieces.

Remove the ribs from the collard greens and slice the greens into thin ribbons.

Finely chop the onion.

Finely chop the carrot.

Finely chop the celery.

Chop the garlic.

Chop the fresh thyme.

Cook the bacon in a large, heavy skillet over medium heat until crisp and the fat is rendered.

Remove the bacon with a slotted spoon and discard all but 2 tablespoons of the bacon fat.

Sauté the vegetables, garlic, and thyme in the hot bacon fat until tender, about 8 minutes.

Season with red-pepper flakes, kosher salt, and freshly ground black pepper.

Set aside the vegetable mixture to cool slightly.

Spread the cornbread cubes on a baking sheet.

Toast the cornbread in the preheated oven for 5-6 minutes, until they brown slightly on the edges.

Put the cubed cornbread in a very large mixing bowl.

Pour the chicken broth and beaten eggs over the cornbread.

Add the vegetable mixture, bacon, and parsley to the bowl.

Toss all ingredients together thoroughly.

Spoon the dressing into the prepared casserole dish.

Cover the casserole dish with foil.

Bake for 30 minutes.

Uncover the casserole dish.

Continue baking for 15 minutes more, to give it a nice crust.