Add the basil, garlic, peanuts, green onions, and red jalapeño into a food processor. Pulse six to ten times until the mixture is roughly chopped.
Then, drizzle in the sesame oil, vinegar, honey, soy sauce, lime juice and kosher salt. Pulse several more times to emulsify the sauce, stopping on occasion to scrape the mixture off the sides with a rubber spatula.
Taste for seasoning, and add more salt or vinegar to taste. Then, add the water chestnuts and pulse a few more times.