Trim off the toenails from the chicken feet and rinse them thoroughly under cold water. Bring a large pot of salted water to a boil, then add the cleaned feet and simmer for about 1 hour until the meat is completely tender and pulls away easily from the bones. Drain the feet and spread them on a cutting board to cool to room temperature, which typically takes 15-20 minutes. Once cooled, carefully remove all the small bones from the feet—the meat should separate easily at this point. Set the boneless chicken feet aside.
In a medium bowl, combine the freshly squeezed lime juice, fish sauce, chili sauce, soy sauce, finely minced garlic, grated ginger, and palm sugar. Whisk everything together until the sugar dissolves completely and the flavors are well integrated. I like to taste the dressing at this point and adjust the balance—if it's too salty, add a touch more lime juice; if it needs more depth, a few extra drops of fish sauce work wonders. Set the dressing aside.
While the dressing sits, cut the celery into 2-inch sticks, slice the tomatoes into wedges, thinly slice or shave the onion into delicate rings, roughly chop the cilantro, and slice the Thai chilies into thin rings after seeding them (remove seeds if you prefer less heat, or keep a few for extra kick). Arrange all the prepped vegetables and aromatics in a large serving bowl.
Add the boneless chicken feet from Step 1 to the bowl with the fresh vegetables from Step 3. Pour the dressing from Step 2 over everything and gently toss until all components are evenly coated. I find that letting the salad sit for a few minutes after dressing allows the flavors to start melding together. Taste and adjust the seasoning if needed—Thai food is all about balance, so don't hesitate to add a squeeze more lime or a drizzle more fish sauce.
Drizzle the salad with the toasted sesame oil and sprinkle the toasted sesame seeds over the top for a nutty aroma and final textural element. Cover the bowl loosely and refrigerate for at least 30 minutes (or up to 2 hours) before serving. This resting time allows the chicken feet to absorb the dressing flavors while the vegetables soften slightly and release their juices.