TO POACH THE CHICKEN (if using rotisserie chicken, skip).
Arrange the chicken, ginger and garlic in a single layer on the bottom of a pot. Scatter the salt over the top.
Pour in enough cool water to cover the chicken by an inch or so.
Place the pot of chicken on the stovetop over medium-high heat. Bring the water to a boil. As soon as the water comes to a boil, reduce the heat to low, cover the pot, and let the chicken simmer. Remove any foam with a spoon that accumulates at the top during the cooking.
Check the chicken after 10 minutes. It is done when no longer pink and an instant read thermometer in the thickest part of the meat registers 170 degrees F. (I find the chicken typically cooks in 10-12 minutes).
Remove the chicken from the liquid and place on a cutting board to cool. When cooled, pull the chicken apart with a fork and set aside.
Meanwhile, heat 1 tablespoon of olive oil in a medium sized pan on medium-high heat. Add the shallots and red pepper and cook for 8 minutes, stirring occasionally.
Add the garlic and cook for a minute more. Remove from heat and set aside.
In a large bowl, mix together the green onions, mint, cilantro and shredded chicken.
In a small bowl, whisk together the fish sauce, lime juice and chili paste. Pour over the chicken mixture and stir.
Spoon into lettuce cups or on top of a bed of lettuce.