First, take the chopped broccoli and bring a pot of water to boil. Season the water with salt and then blanch the broccoli in the hot water and turn off the stove. While preparing the other ingredients allow the broccoli to soften.
Next, slice up the chicken breast into small chunks. Do not make them too big because you want the chunks to cook fast and all the way. Season the chicken chunks with salt and pepper after cutting.
In a frying pan on medium high heat add a little oil and sauté the chicken chunks. As the chunks finish cooking toss them to the side in a plate.
Now, you want to prepare the sauce and the ziti at the same time. Cook the ziti according to the directions on the package.
While the ziti is cooking, melt butter on medium heat in a pot big enough for the entire recipe, a dutch oven is perfect.
Now, once the butter has melted toss in the flour. Using a spoon, cook the flour with the butter. A paste should start to form, there will also be some bubbling. This is cooking the raw flavor from the flour.
Next, slowly pour in milk. Slowly pour in because if you pour too fast lumps could happen. You want to make sure the milk is mixing perfect with the flour. After you have added all the milk pour in the evaporated milk.
Allow the sauce to simmer and start to boil a bit. Now, add in the grated cheese. Using your spoon, swirl everything around until the cheese has melted into the sauce. Once the cheese has melted turn off the heat.
Then, season the sauce with salt, pepper and squeeze a lemon into the cheese sauce.
Lastly, once the ziti is finished, drain it immediately and add into the sauce. Then, add in the cooked chicken and drained broccoli. Toss everything together then taste for seasoning before serving.