Heat 1 teaspoon of the sesame oil over medium-high heat in a deep skillet. Add ginger, garlic and chili paste. Heat until fragrant, about 30 seconds, then add in the beef.
Using a wooden spoon, begin breaking the beef up into bite-sized pieces. Saute until beef is browned, about 7-9 minutes. While the beef is browning, whisk together the soy sauce, rice vinegar, hoisin and chicken broth in a small bowl. Pour mixture over the browned beef and cook until warmed through, about 2 additional minutes. Drizzle with the second teaspoon of sesame oil before serving.
To serve, scoop a small amount of the beef mixture into individual lettuce cups. Sprinkle with scallions or minced peanuts to serve.