In a large saute pan, melt butter over medium high heat. Add mushrooms and shallot and cook until golden brown, only stirring a few times to evenly cook, about 5 minutes.
Add spinach, stir, and cover with lid. Reduce heat to low and cook until spinach is completely wilted, about 3-4 minutes. Remove from pan and allow mixture to cool.
On the meaty side of each chop, slice through the middle of the meat to the bone to create a pocket. Add your sliced provolone to the inside of the chop. Divide the spinach mixture evenly between the four chops and stuff them. Hold opening together with toothpicks, if needed.
Add salt and pepper to the outside of your chops.
Preheat oven to 375 degrees F.
Using an oven safe skillet, heat olive oil over high heat. When the oil is hot, cook the pork chops until lightly golden brown, about 2 minutes. Flip the chops and transfer the pan to the oven to finish cooking. Cook until the internal temperature of the meat reaches 155 degrees F, about 15 minutes.