Char the peppers over an open flame or under a hot broiler and blacken skins evenly all over. Place in a bowl; cover and cool to handle. Peel the skins and seed the peppers, then quarter them lengthwise and slice 1/4- to 1/2-inch thick.
Heat deep skillet or large Dutch oven over medium-high heat with 3 tablespoons olive oil, three turns of the pan. Add caraway and cumin, and stir 30 seconds; add mushrooms and brown until very tender and beefy in aroma. Add the onions, garlic, salt, pepper, herbs and paprika and cook, partially covered, for 6-7 minutes more to soften the onion, stirring frequently. Add the sherry to deglaze the pan, then the stock and tomatoes. Reduce the heat and simmer gently until ready to serve.
Bring a large pot of water to a boil for the egg noodles. When the water boils rapidly, add the salt and noodles or pasta and cook to al dente. Reserve 1/3-1/2 cup of the starchy cooking water just before draining. Drain the noodles or pasta and return to the pot. Toss the noodles or pasta with pasta water, butter, herbs, salt and pepper.
Stir the crème fraiche into the paprikash and remove from heat. Serve the paprikash over a bed of herb egg noodles or pasta.