Start by heating a large pot of water on high heat so it will be boiling when it’s time to cook the pasta.
While the water’s heating, slice the chicken breasts cutting them in half lengthwise so they are half as thick. Place them between sheets of wax paper and pound until tender. Season the chicken breasts with salt and pepper.
Spread the flour on a plate. Dredge the chicken breasts in the flour until well covered. Set aside.
Add 2 tablespoons of butter and 2 tablespoons of olive oil to a frying pan. When sizzling, add 3-4 chicken pieces or as many fit without overcrowding.
Cook on medium-high heat for 3-4 minutes until browned and then turn over and cook on the other side. Remove the chicken breasts from the pan and set aside. Add 2 more tablespoons of butter and olive oil and cook the remaining chicken breasts. Set aside.
Add the lemon juice, chicken stock, and capers to the pan with the butter and olive oil. Simmer for a few minutes adding 2 more tablespoons of butter. Pour the sauce into a small saucepan and keep warm.
Add the pasta to the boiling water and cook for 4 minutes for fresh pasta or as directed on the package for dried pasta.
In the frying pan that had the sauce, add the mixed greens and heat on low. Cover with a lid and cook for a few minutes until wilted.
Assemble your plates by spooning one serving of pasta, and a large spoonful of the mixed greens on each plate. Add a piece of chicken and spoon the sauce over the top.