Wash the zucchini, remove the stems and cut crosswise. Then, cut zucchini slices approximately one centimeter thick.
Crush the garlic and season the chicken with 3 garlic (reserve 1 garlic clove), Italian herbs, salt, and pepper.
Place the flour with a pinch of salt on a flat plate, mix the bread with the Parmesan cheese and place it on a second flat plate. Finally, beat the egg, add the last crushed garlic and a pinch of salt, place the egg in a medium bowl.
Breaded the chicken supremes: pass the chicken supremes first through the flour, then through the egg and finally through the mixture of bread and Parmesan cheese.
When the chicken supremes are breaded, place them on a plate while arranging a medium pan with the butter and oil. Bring the pan to the stove over medium-high heat and fry the chicken breasts until they are golden brown on all sides.
Then add the zucchini, lower the heat to medium-low and let cook about five minutes over low heat. Stir a little so that the zucchini brown, being careful not to damage the breaded chicken. When the zucchini begins to toast, the chicken will be ready.
Remove the pan from the heat, serve two or three tablespoons of zucchini with a chicken supreme. Sprinkle with a little parsley if desired.