Melt 1 tablespoon of butter in your pan, and heat until sizzling. Quickly saute the zucchini slices on one side until they get a bit of color on them, and remove from heat. Melt another tablespoon of oil in the pan and let it heat up over medium to medium high heat. Season the chicken liberally with salt and pepper, and place into the hot pan. Don't move the chicken for several minutes. You want the chicken to get brown. Try to resist! The trick is not letting it burn. Use your nose, and smell. You can also check a piece here and there, but for the most part try to leave it alone as much as possible.
Once the chicken is browned flip it and brown the other sides. Once the chicken has browned, toss in the garlic and cook for 1 minute.
Remove the chicken from the pan and set aside with the zucchini. Put the remaining butter into the pan along with the flour. Whisk until lumps are gone, and add the wine and continue whisking until evenly combined. Add in the half and half, and reduce heat to medium-low. Simmer until sauce is thickened. Add back in the chicken, basil, and zucchini and simmer for 5 minutes. Mix in with the pasta, place in a baking dish, and stir in a cup of mozzarella cheese. Bake at 325 for 15-20 minutes, or until the cheese is melted.