Preheat your oven to 350.
Heat 2 Tbs. butter and 1 Tbs. oil in a wide pan. Once melted, add the sliced mushrooms and chopped rosemary. Let it sauté for two minutes, then sprinkle with a pinch of coarse salt. After another two minutes of browning, add the spinach and let wilt. Remove mixture from the pan and give it fine chop.
Take the pork tenderloin and butterfly it with a sharp knife. Meaning, take a knife and slice it through the center, width-wise, but not all the way through! Open the pork like a book, and place plastic wrap over the top. Pound it out, from top to bottom until thin. Season the pork with salt and pepper.
Overlap the provolone cheese down the center of the pork, and evenly spoon the filling over the cheese. Give one more sprinkle of salt over the filling, then gently roll the pork, from side to side, shoving the filling back inside as best you can. Secure the pork with a few pieces of twine, up and down the stuffed tenderloin. Season the outside with salt and pepper.
To the pan, add 3 Tbs. of butter. Once it’s melted and foaming, gently place the pork in the pan let sear for three minutes on medium high. Not too high or the butter will burn. After three minutes, rotate the pork a little bit, and sear three more minutes. Keep searing in three-minute chunks until the pork is browned all over. Tip the pan every few minutes and spoon the butter over the pork, basting it with extra browned butter flavor. Add the last tablespoon of butter to the pan and slide the pork into the oven for 8-10 minutes, until cooked through.
Let rest on a cutting board for five minutes, then cut into one-inch slices, fanning on a platter. Garnish with chopped parsley and extra rosemary if desired!