To make the vinaigrette, whisk the vinegar, fish sauce, sugar and pepper flakes together. Slowly drizzle in the oil while whisking continuously. Set aside 1/2 cup for the marinade.
Marinate the diced pears in 1/2 cup vinaigrette for at least 1 hour.
To serve, toss 2 cups romaine and 2 tablespoons carrots per serving with 1 tablespoon vinaigrette. Mound the greens on a plate and top with 1/2 cup marinated diced pears. Sprinkle the top of the salad with the chopped peanuts and mint, scatter a few fried egg roll strips on top and garnish with a mint sprig if desired.