Remove any silverskin from the pork tenderloin.
Cut the pork across the tenderloin into 3/4 inch medallions.
Pound the medallions to 1/4 inch thick.
Season both sides of the pork with salt and pepper.
Heat a heavy skillet over medium heat.
Add one Tbsp butter and one Tbsp olive oil.
Dredge the pork in the flour and fry until the edges start to turn white, about 60-90 seconds. Only add as much as will fit comfortably in one layer.
Flip and cook another 45 seconds to one minute. You don't want to overcook the pork.Remove pork from pan.
Add remaining Tbsp olive oil and repeat with the remaining pork.
Deglaze the pan with the lemon juice, stirring constantly. When it has almost completely evaporated add the chicken stock and simmer for about 1 minute.
Return the pork and accumulated juices to the pan to warm up the pork. Simmer about a minute. The flour from the pork will thicken the sauce slightly. Add the capers.
Off heat add the remaining one Tbsp butter to enrich the sauce. Jostle the pork around a bit to distribute the butter. Awkward but easier than removing all the pork. Adjust seasoning.
Sprinkle with Italian parsley.