Cut the pork tenderloin into 1-inch-thick steaks on a long bias. Season the steaks all over with salt and black pepper, then toss in the flour to coat.
Melt 2 tablespoons of the butter in a large skillet over medium-high heat until the foam subsides. Shake the excess flour off the meat and add it to the skillet. Cook, flipping once, until cooked to medium and an instant-read thermometer inserted into the center registers about 150 degrees F, about 4 minutes per side. Remove the pork steaks to a platter and lower the heat under the skillet to medium.
Add the remaining 1 tablespoon butter and the shallots. Cook, stirring, until softened, about 2 minutes. Add the cider, mustard, parsley, chives and a sprinkle of salt and black pepper. Simmer, scraping up any brown bits, until reduced by about half, about 2 minutes. Top the steaks with the sauce and serve.