Make spaetzle first: Combine the milk, eggs, salt and nutmeg in the container of a food processor or blender. Blend until smooth, about 30 seconds. Add flour and blend for another 30 seconds, or until smooth. Batter will be thick and sticky.
Bring a large pot of salted water to a boil. Pour some of the batter into a potato ricer held over the boiling water. Press through to form strands. Stir gently as it hits the water to prevent sticking. Simmer until the spaetzle float to the surface then remove with a slotted spoon to a large buttered baking dish. Continue with remaining batter. This can be done up to 2 hours in advance. Let stand at room temperature.
On a sheet of waxed paper or paper plate, combine the flour, salt and pepper. Coat the chicken in the mixture, patting off the excess to leave a fine even film. Reserve excess flour. Melt 2 tablespoons of butter in a large skillet over medium-high heat. Add olive oil. When bubbling hot, add the chicken with the skin side down. Cook until golden brown, turn and cook until browned on the other side. Transfer to a platter and tent with aluminum foil to keep warm.
In a separate skillet, melt 2 tablespoons of butter over medium-high heat and add 1 tablespoon of olive oil. Add the chicken livers and cook, without moving, for about 2 minutes per side. Livers should still be pink in the middle. Transfer to the platter with the chicken.
Wipe out the first skillet with paper towels. Add 2 tablespoons of butter and 1 tablespoon olive oil. Heat over medium-high heat until bubbly and hot. Add cherries, port wine and chicken stock and bring to a simmer. Cook until reduced by a third. Stir together the cornstarch and cold water; stir into the sauce and cook until thick. Add the chicken breasts, skin side up. Tilt pan and spoon sauce over them. Add chicken livers to the skillet and turn to coat each one with the sauce. Keep warm over low heat.
Melt 1/2 cup butter in a large skillet over medium heat until golden brown, about 3 minutes. Add spaetzle and toss until heated through. Season to taste with salt and pepper.
To serve, pile spaetzle on a large platter and top with the chicken and sauce.