Preheat the oven to 400 degrees F.
Remove the outer leaves from cauliflower and discard, leaving the core intact. Place the cauliflower, base side down, on a cutting board. Cut the cauliflower head in half, down the center, using a sharp knife. Cut each half into two ¾"-thick slices. Set "steaks" aside.
In an oven-proof skillet, heat 2 tablespoons olive oil over medium-high heat. Add the cauliflower steaks, working in two batches. Season with salt and pepper and sear 2 to 3 minutes per side.
Place the skillet in the oven and roast cauliflower until golden brown, 15 to 20 minutes.
Meanwhile, in a sauté pan, heat the remaining 1 tablespoon olive oil over medium heat and sauté the mushrooms until golden brown, about 4 minutes. Remove the mushrooms from the sauté pan and set aside. Add 1/4 cup of water or vegetable broth to the pan. Scrape up the browned bits from the bottom of the pan, add the flour to the liquid and bring to a boil, whisking vigorously. Add the mushrooms back to the sauté pan and coat the mushrooms with the gravy. Season to taste with salt and pepper.
Remove the cauliflower from the oven, top with mushroom gravy and sprinkle with chopped parsley.
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