Preheat a 3- or 5-qt. sauté pan over medium-high heat until rim of pan is hot to the touch. Add oil and heat for about 1 more minute.
Add pork and cook, turning as needed, until browned on all sides, about 4 minutes.
Transfer meat to a 9x13-in. baking pan and bake in a 400°F/205°C oven until a meat thermometer inserted in thickest part of tenderloin registers 160°F/75°C, about 15 minutes.
Meanwhile, discard fat from sauté pan and add port and broth. Bring to a boil over high heat and boil, uncovered, until reduced to about 3/4 c. (about 3 minutes).
Stir in milk and continue to boil, stirring, until sauce is covered with large, shiny bubbles (about 5 more minutes).
Add cheese and stir until melted; stir in chilies, if desired. Remove from heat.
To serve, thinly slice meat across the grain. Fan out slices on individual plates and spoon sauce over them.