Vietnamese Chicken Sandwich (Banh Mi)

1 carrot , peeled

1/2 cup rice vinegar (not seasoned)

1 tablespoon sugar

1 (24-inch) soft baguette

2 tablespoons vegetable oil

1 tablespoon Asian fish sauce

1/2 teaspoon soy sauce

1/4 pound liverwurst

2 fresh jalapeños, thinly sliced

1/2 sweet onion , cut into 1/4-inch rings

3/4 cup packed cilantro sprigs

2 cooked chicken breasts from a rotisserie chicken, thinly sliced

Lettuce leaves

2 tablespoons mayonnaise