Place the mushrooms in a small pot and cover with the stock. Bring to a low simmer and reconstitute the mushrooms.
Bring a medium pot of salted water to boil.
Sprinkle the chicken with salt and pepper and then dredge in some flour. Heat the oil in a large skillet over medium-high heat. Add the chicken and brown on both sides, then transfer to a plate. Melt 4 tablespoons of the butter into the oil and add the carrots, garlic, shallots and some salt and pepper, and cook partially covered to soften the vegetables, 5 minutes. Deglaze the pan with the brandy then stir in the wine. Remove the mushrooms from the stock and chop. Add the mushrooms to the pan along with most of the soaking liquid; discard the last few spoonfuls where grit may have settled. Add the tomatoes and tarragon, and then slide the chicken back in and simmer to thicken a bit, 10 minutes.
Cook the noodles until al dente in salted water, then drain the noodles and add the remaining 1 tablespoon butter, and toss to coat. Serve the chicken pieces with the buttered egg noodles and a few spoonfuls of the sauce alongside.