Preheat oven to 375 degrees. Line a large baking tray with foil or parchment paper; set aside.
Place chicken between 2 sheets plastic wrap. Using a rolling pin or mallet, pound until about 1/4 inch thick.
Place flour on a shallow plate. Lightly whisk milk or water and eggs together in a shallow bowl. Place breadcrumbs on a separate plate.
Season cutlets with salt and pepper. Coat 1 piece chicken in flour, shaking off excess. Dip in egg mixture. Coat in breadcrumbs, pressing on to secure. Place on prepared tray. Repeat with remaining chicken, flour, egg mixture and breadcrumbs.
Heat olive oil and butter in a skillet over medium heat. Add chicken cutlets and cook about 3-4 minute per side. These will be placed in the oven; it's okay to be slightly undercooked. Place the browned cutlets on the prepared baking sheet.
Divide the pasta sauce equally over the chicken. Arrange the avocado over sauce. Sprinkle with cheese. Bake for 5 to 7 minutes until cheese is melted.