Place a chicken breast on a cutting board. Rest your one hand on the top of the chicken breast. Use a long sharp knife to slice the chicken breast in half so you have two thinner cutlets of chicken. Place a piece of plastic wrap over one chicken cutlet and pound it so that it is an even thickness. Flatten the other cutlet the same way. Do this with the remaining chicken breasts.
Place the cutlets on smoker racks and cold smoke (smoke only with no heat) for 20-40 minutes (20 minutes for slightly smoky and 40 minutes for more distinct smoky flavour).
Remove from smoker and brush with a little oil to moisten the surfaces, dredge chicken cutlets in panko bread crumbs.
Heat oil in a skillet over medium heat. Place the breaded chicken cutlets in the skillet and fry until cooked through, flipping hallway. Since these cutlets are thinner than a whole chicken breast, it will take less time to cook through, usually around 8-10 minutes. Depending on the size of the skillet, all the cutlets might not fit, so you may need to cook them in batches.
Remove the chicken cutlets from the skillet, for now, and place on a plate. Add the vegetables to the skillet and pour in the water. Cover with a lid and allow the vegetables to steam. Check every once in a while and stir so they do not stick or burn on the bottom of the skillet. Continue to cook until the broccoli is tender, probably around 6-7 minutes.
Remove the vegetables, for now, from the skillet and place in a large bowl. Melt the butter in the skillet and whisk in the flour to create a roux. Slowly whisk in the buttermilk, parmesan cheese, dill, salt and pepper. Lower heat and let simmer for 3-4 minutes.
Add the vegetables and chicken back to the skillet and gently stir to coat in the sauce.