Roast peppers under broiler with oven door slightly ajar to allow steam to escape. Place charred peppers in a bowl and cover with plastic wrap. Let cool to handle; peel and seed. Place peppers in a food processor with onion, parsley, garlic, thyme and chicken stock. Pure until smooth.
Preheat oven to 375F.
Bring a pot of water to a boil for the noodles.
Melt 3 tablespoons butter in a medium saucepot over medium heat. Whisk in flour, cook 1 minute then whisk in milk and season with salt and pepper. Stir in sour or heavy cream and thicken sauce. Combine with paprika and pepper pure.
Meanwhile, heat 2 tablespoons EVOO, 2 turns of the pan, over medium-high heat in a large skillet. Season chicken with salt and pepper, and brown on both sides. Transfer to a shallow baking casserole, top with sauce and cheese, and bake 20-25 minutes to finish cooking chicken through and brown the top.
While chicken is in the oven, cook egg noodles to al dente. Drain and return them to the hot pot. Toss with remaining 3 tablespoons butter cut into small pieces and season with salt, pepper, poppy seeds and chives.
Serve chicken with egg noodles alongside with extra sauce poured over the top or passed at the table.