Rinse meat and pat dry. If needed, cut tenderloin in half crosswise to fit a 10- to 12-inch frying pan.
Place empty frying pan over high heat. Add oil; when hot, add tenderloin and turn as needed to brown well on all sides, 5 to 8 minutes total.
Reduce heat to medium-low. Add vermouth, rosemary, thyme, and pepper. Cover and simmer, turning pork after 5 minutes, until a thermometer inserted in thickest part reaches 155°, 10 to 12 minutes total. Transfer pork to a platter and keep warm.
Measure pan juices. If less than 1/2 cup, add broth to make 1/2 cup. If more than 1/2 cup, boil on high heat, uncovered, until reduced to 1/2 cup.
Blend milk and cornstarch. Mix into pan and stir over high heat until boiling. Add salt to taste. Pour into a bowl.
Cut pork into diagonal slices and pour sauce around or over meat.