Heat the oven to 425 degrees. Pluck 1 tablespoon leaves from the rosemary sprigs (reserve the rest). Using a mortar and pestle or knife and cutting board, combine the rosemary leaves, 3 garlic cloves, the fennel seeds (if using) and a pinch of salt and pepper. Pound or chop until a coarse paste forms. Season the pork with salt, then coat with the garlic-rosemary mixture. (You can season and refrigerate the pork up to 8 hours ahead.)
Heat the oil in a large, oven-proof skillet over medium-high. Add the pork and scatter the mushrooms around (skillet might be snug). Sear until browned underneath, 4 to 5 minutes. Season the mushrooms with salt and pepper and add the butter, remaining garlic clove and the reserved rosemary sprigs. Flip the pork, stir the mushrooms and spread them to fill the skillet. Roast, stirring the mushrooms halfway through, until a thermometer inserted into the thickest part of the pork registers between 140 and 145 degrees, 10 to 12 minutes.
Transfer the pork to a cutting board to rest at least 5 minutes. Stir the vinegar into the mushrooms and scrape up any browned bits stuck to the bottom of the skillet. Thinly slice the pork and serve with the mushrooms, spooning the pan drippings over top.
