Heat oil and butter in a large heavy pot over medium-high heat. Add the mushrooms and cook for 8-12 minutes, stirring often, until well-browned and softened. Season with salt and pepper and transfer to a bowl.
Cook the Mirepoix:
If the pot is too dry, add another drizzle of oil. Add the onion, carrots, and celery and cook for 5-7 minutes until just beginning to soften. Add the garlic and cook for 45 seconds.
Add the diced Roma tomatoes and the barley and cook for 1 minute, stirring regularly. Return the mushrooms to the pot and stir.
Add the Stock:
Sprinkle the flour over the dish and stir to combine. Cook, stirring often, for 2-3 minutes until the flour deepens in color. Be careful not to burn the flour.
Pour in 1 cup of stock and whisk to combine. Continue adding the stock, one cup at a time, whisking after each addition until all the stock is added. Season with chives, thyme, and parsley. Add the crushed red pepper and season again with salt and pepper to taste.
Bring to a boil and then reduce heat and simmer for 25-30 minutes until the barley is tender. Stir regularly and add up to 2 cups more stock if necessary. Taste and season again to preference.
Fry the Mushrooms:
Once the stew is ready to serve, crisp up the mushroom topping.
Heat the oil in a skillet over high heat. Once very hot, add the mushrooms and cook without moving for 2-3 minutes until very well browned. Flip and cook an additional 1-2 minutes until well-browned on the other side. Turn off the heat.
Transfer the mushrooms to a bowl with freshly minced parsley and sprinkle immediately with flaky sea salt. Toss to coat with parsley.
To Serve:
Divide the mushroom barley stew between bowls and pile the crispy mushrooms on top. Garnish with any remaining parsley. Enjoy!
Notes
I used young, small carrots which did not need to be peeled. If using larger carrots, you only need 3 carrots. Peel them first.