Char the peppers on the stovetop or under the broiler with the oven door cracked for the steam to escape. Place the charred peppers in a bowl and cover with plastic wrap to cool. Scrape or peel the skin from the peppers, then seed, and thinly slice.
Heat 1/4 cup extra-virgin olive oil in a large Dutch oven or large, deep skillet over medium-high heat. Add the mushrooms and brown 12 to 15 minutes until darkened and tender. Add the Fresno peppers, onion, carrot, garlic, paprika, salt, and pepper, and cook to soften, 10 minutes more.
Add the tomato paste to the vegetables and stir 1 minute. Add the stock, wine, Worcestershire sauce, and roasted red peppers. Simmer a few minutes for the flavors to combine, then cool completely and store for make-ahead meal.
Reheat the mushrooms and sauce over medium heat, stirring occasionally.
In boiling salted water, cook the egg noodles or egg pasta to al dente and toss with butter and herbs.
Stir a few spoonfuls of sour cream into the paprikash and serve in shallow bowls on a bed of noodles or pasta.