Cook bacon in a braiser pan or large skillet over medium until browned, 7 to 9 minutes. Drain on paper towels. Discard fat from pan.
Season chicken with salt and pepper. Melt 2 tablespoons butter in pan over medium-high. Add chicken, skin-side down; cook, turning a few times, until browned all over, 10 to 12 minutes. Transfer to a plate.
Melt remaining 1 tablespoon butter over medium. Add mushrooms and shallots; season with salt. Cook, stirring and scraping up browned bits, until golden brown in places, 8 to 10 minutes.
Add broth and cream; bring to a boil. Stir in noodles. Add chicken, skin-side up, and accumulated juices to pan.
Cover, reduce heat, and simmer, stirring once halfway through, until chicken is just cooked through, 10 to 12 minutes.
Uncover; simmer until thickened, 2 to 3 minutes. Stir in dill and top with bacon. Serve, with more dill.
