Cut potatoes in half or quarters, and toss in 3 TBSP. of the butter, 1 TBSP. ranch powder, salt, pepper, and 2 TBSP. parmesan. Spread on the sheet pan and roast 10 minutes.
Combine the flour and egg. On a plate, combine the breadcrumbs, 2 TBSP. ranch, and 2 TBSP. parmesan. Dredge the pork chops in the egg mixture, then breadcrumbs. Place on sheet pan.
Mix the green beans with 1 TBSP. butter and salt and pepper. Place next to the pork chops. Roast 15-20 minutes, or until the pork is cooked through.