Preheat oven to 400°.
Combine first 4 ingredients in a small bowl; add 1 teaspoon oil. Rub over pork. Let stand 15 minutes.
Heat the remaining 2 teaspoons of oil in a large oven-proof skillet over medium-high heat. Add pork; cook 4 minutes, browning on all sides. Bake at 400° for 10 minutes or until a thermometer registers 160° (slightly pink). Let stand 5 minutes. Remove pork from pan; cut diagonally across grain into 12 slices.
Return pan to medium-high heat, and add broth, scraping pan to loosen browned bits. Add sherry and tomato paste; stir with a whisk. Bring to a boil. Reduce heat; simmer 5 minutes.
Cut rolls in half horizontally. Place 2 slices pork on bottom half of each roll; top with lettuce leaf, if desired. Cover with roll tops. Serve with jus.