Between two sheets of plastic wrap, place chicken breasts. Pound with meat cleaver until chicken breasts are 1/2" in thickness. Set aside.
In large, non-stick skillet over medium-high heat, warm 1 tablespoon butter and vegetable oil. Add chicken; saute for 4-5 minutes on each side, until nicely browned and cooked through. Remove chicken, set aside and cover with foil to keep warm.
To same pan, add carrots, leeks and celery. Saute until browned and very soft, about 4 minutes. Add apple brandy to pan, ignite with match and let flames subside. Pour in cream, reduce heat to low and bring mixture to simmer. Cook until cream is slightly thickened and reduced, about 3 minutes. While sauce is cooking, place spinach leaves in saucepan with second tablespoon of butter. Add salt, pepper and nutmeg to spinach; cook over low heat about 2 minutes to wilt.
To serve, spoon one-fourth of spinach in the middle of each of 4 individual plates. Place chicken breast on top of spinach. Spoon sauce and vegetables over chicken and serve immediately.