Place cast iron skillet on medium heat, add 2 T olive oil.
Crack 1 egg into a shallow bowl, whisk with a fork. Pour 2 T breadcrumbs and 1 teaspoon Italian seasoning into another shallow bowl. Dip pork chop into egg, flip and cover entire pork chop with egg.
Repeat with bread crumbs. Bread with breadcrumbs on both sides. Leave remaining breadcrumbs in the shallow dish. Once skillet is hot, place pork chop on skillet. Set a timer for 6 minutes. Add 1 med Yukon gold potato, cubed to skillet. Stir potatoes occasionally.
Flip pork chop once timer goes off, set timer for 6 minutes to cook the second side. Add 1 large handful sliced green beans and remaining breadcrumbs (from shallow bowl) to pan. Cook until pork is done, or to 145 degrees in the center.
Add vegetables and pork chop to plate. Top with a squeeze of lemon, 1 T parmesan cheese, and salt & pepper to taste. Let pork rest for at least 5 minutes before cutting into it.