Place the porcini mushrooms and stock in a small pot. Bring to a low simmer to reconstitute the mushrooms. Remove from heat and reserve.
Bring a medium pot of water to a boil.
Season the chicken with salt and pepper and dredge in flour. In a large skillet, heat the EVOO over medium-high. Add the chicken and cook until browned on both sides and cooked through, 3-5 minutes; transfer to a plate. Reduce the heat to medium, melt 3 tablespoons butter in the skillet and add the carrots, shallots and garlic. Season with salt and pepper. Partially cover and cook until the vegetables are softened, 3-5 minutes.
Deglaze the pan with the brandy, then stir in the wine. Remove the mushrooms from the stock and chop; add to the pan along with the stock, discarding the last few spoonfuls where grit may have settled. Add the tomatoes and tarragon. Add the chicken and simmer until sauce thickens a bit, about 10 minutes.
Meanwhile, salt the boiling water and cook the egg noodles until al dente. Drain the noodles, return to the pot and toss with the remaining 1 tablespoon butter. Serve the chicken with the buttered egg noodles and a few spoonfuls of sauce.