Prepare the ingredients: cut mushrooms into thick slices, butternut squash into very small cubes (1/4-1/3 inch or 5-7mm), dice the onion, finely chop garlic, and dill.
Prepare the chicken: cut the chicken breasts in half horizontally so you have 4 thinner cutlets. Pound each cutlet in its thickest part slightly. Season with salt and pepper on both sides. Dredge in flour on all sides, shake off excess flour.
Cook the chicken: Heat the oil in a large frying pan over high heat, add in the chicken pieces. Cook for about 3 minutes, until golden, turn over and cook for further 2-3 minutes or until browned and cooked through. Transfer to a plate.
Prepare the sauce: Add the mushrooms and butternut squash to the pan in an even layer. Cook over high heat for about 2 minutes without stirring letting them brown at the bottom. Start stirring and cook for about 1 minute. Reduce the heat to medium-low and add onion, cook for 2-3 minutes or until softened. Add garlic and cook for 30 seconds.
Add the cream, broth, and nutmeg, cook over medium-low heat for a few minutes, until the sauce is thickened and butternut squash soft. Don‘t worry if the sour cream breaks into small clumps – the sauce will be smooth again after cooking it for a few minutes.
Assemble: Season the sauce with salt and pepper, stir in chopped dill. Place the chicken in the sauce to warm up. Serve.
Enjoy!