Thinly slice the celery roots and potatoes - I used the thickest adjustment on a small hand-held mandolin. You should have around 5 cups celery root and 3 cups potatoes. Place in a large bowl of cold water and a healthy squeeze of lemon.
Heat the oil in a large heavy pan over medium-high heat and sauté the onion, celery, carrot, and leeks until softened, about 10 minutes. Add the collard greens and cook for another 5 minutes. Stir in the cooked barley.
Warm up the half & half and broth. Add the remaining ingredients. Simmer to reduce by 1/2 cup, about 15 - 20 minutes. You should end up with 2 1/2 cups of *sauce*.
Place a layer of celery root and potatoes on the bottom of the baking dish. Cover with the barley mixture, and top with another layer of celery root and potatoes. Pour the sauce over the whole dish. Cover with foil, and bake for 30 minutes. Remove the foil and bake another 15 minutes, occasionally basting as necessary.