Special equipment: A deep-fry thermometer
Position an oven rack at the top of the oven, and preheat the broiler. Arrange the mushrooms on a baking sheet, and broil until the sides facing up begin to soften, about 5 minutes. Flip, and continue to broil until the sides facing up are soft, about 5 minutes more. Let cool.
Put the mushrooms, gill-side up, between 2 pieces of plastic wrap, and pound to about 1/4 inch thick with a meat mallet. Season all over with 1/2 teaspoon salt.
Whisk together the flour, baking powder and 1 teaspoon each salt and pepper in a shallow dish. Whisk together the milk and eggs in a separate shallow dish.
Lower the oven heat to 250 degrees F. Put a rack over a rimmed baking sheet. Heat about an inch of oil to 350 degrees F in a large cast-iron skillet or Dutch oven over medium-high heat.
While the oil heats, dredge each mushroom in the flour mixture to completely coat; shake off any excess. Then dip into the egg mixture until fully coated; let the excess drip off. Return the mushroom to the flour mixture, and dredge a second time, until completely coated, pressing firmly into the flour mixture. Arrange on one side of the rack on the baking sheet.
Add 2 of the breaded mushrooms to the hot oil, and cook, turning once, until crisp and golden, about 5 minutes total. Transfer the mushrooms to the unused side of the rack. When the oil comes back to temperature, repeat with the remaining 2 mushrooms and keep the first 2 warm in the oven.
Serve the mushroom steaks with mashed potatoes and generous spoonfuls of hot gravy. Garnish with chives or scallions if using.
Position an oven rack in the top position in the oven and preheat to 450 degrees F. Toss the onions, celery, carrots and garlic with the oil and 1 teaspoon salt on a rimmed baking sheet. Roast until the vegetables are charred in some places, 25 to 30 minutes.
Bring the roasted vegetables, 1 cup water, mushrooms, thyme, sun-dried tomatoes, soy sauce, bay leaf and 1 teaspoon salt to a simmer in a medium saucepan over medium-high heat. Cook, stirring occasionally, until most of the liquid is gone, 8 to 10 minutes. Add 6 cups water and 1/2 teaspoon salt, and bring back to a simmer. Reduce the heat to medium-low, and gently simmer until reduced by about one third, about 45 minutes. Strain the stock into a large liquid measuring cup, then squeeze all the liquid out of the solids with the back of a ladle (there should be about 4 cups of stock); discard the solids. (If not making gravy right away, let the stock cool to room temperature, then refrigerate for up to 3 days or freeze for up to 1 month; warm slightly before making gravy.)
Melt the butter in a medium saucepan over medium heat. Add the sage leaves to the butter, and stir for 30 seconds; remove the fried sage leaves, and set aside. Add the flour to the saucepan, and stir until smooth and lightly golden, about 2 minutes. Slowly pour in the warm stock while whisking constantly until smooth and thick, 8 to 10 minutes.
Chop the fried sage, stir it and the parsley into the gravy and season to taste with pepper.
Copyright 2014 Television Food Network, G.P. All rights reserved.