Rub salt and pepper over all sides of pork tenderloins; nestle tenderloins next to each other in a 9×13-inch baking dish.
Melt butter in a saucepan over medium heat; add garlic and mushrooms. Bring to a boil, reduce heat to medium-low, and simmer, stirring frequently, until sauce is fragrant, about 5 minutes. Stir vinegar into mushroom sauce. Pour mushroom sauce over tenderloins, letting sauce seep between the two tenderloins.
Bake in the preheated oven until tenderloins are lightly pink in the center, about 45 minutes. An instant-read thermometer inserted into the center should read at least 145 degrees F (63 degrees C). Transfer tenderloins to a serving dish.
Drain the drippings, including mushrooms, from the baking dish into a measuring cup, scraping the bottom to get all the brown bits. Remove 1/4 cup of the fat from the mixture and pour into a saucepan. Add enough chicken broth to the drippings to make 2 cups; whisk flour into drippings until incorporated. Stir broth-drippings mixture into the saucepan with fat over medium heat until thickened, about 5 minutes; season with salt and pepper.
Slice tenderloins into medallions and top with half the gravy. Pour the remaining gravy into a gravy boat for serving.