Cut your chicken into strips about 1" wide and 4" long, season with salt and pepper, set aside
In a small bowl or dish, combine the 1 cup grated parmesan cheese and ½ cup All purpose flour and season with salt and pepper. Stir to combine
Set up a dredging station, first the 1 lg egg and 1 T water in a bowl, then the parmesan cheese and flour mixture
One piece at a time, dip the chicken strips into the egg wash, then into the parmesan and flour mixture and coat evenly, set aside on a plate or tray and continue until all of the chicken has been coated with the cheese mixture.
In a large frying pan on the stovetop, add the 3 Tbsp olive oil and the3 Tbsp butter and melt over medium heat.
Once the oil and butter is hot, add the chicken strips and working in batches if necessary, cook the strips until golden brown on both sides and place them into the casserole dish as they are done. When about half of the strips are cooked, spoon about 1 cup of the sauce over them in the casserole dish.
Once all of the chicken is done and in the casserole dish, spoon the remaining sauce mixture over the top, covering all of the chicken, then sprinkle the top with 2 cups shredded swiss or gruyere cheese (more or less as you desire)
Bake in 350℉ oven for 30 minutes uncovered, until the cheese is bubbly and slightly brown on top. Serve over rice.