Cut the melanzani into slices. Cut peppers into strips.
Preheat stove to 180 degrees. Heat butter in a frying pan.
Add melanzani and season well. Saute over medium heat for 5 min with lid closed until soft. Add green and red bell pepper strips, mix and season. Continue to steam over medium heat for 5 min.
Place vegetables in a baking dish. Cover with aluminum foil and place in stove for about 5 to 6 min. Heat oil in the same frying pan. Sauté pork chops (meat should be stalked and nicely marbled) in it for 5 min. at high temperature.
Turn meat to the other side and reduce temperature a tiny bit. Season well and sprinkle with paprika, continue frying for about 10 min.
Bring pork chops to table with eggplant mixture and bearnaise sauce.