In a large bowl, whisk together the lime, fish sauce, soy sauce, sweetener, and garlic. Stir in the white/light green parts of the scallions and let it sit for 5-10 minutes.
Add the chicken, cabbage, carrot, mint or basil, cilantro, jalapeno, and the remaining scallions and toss to coat.
To make the topping (if using), in a medium to large skillet over medium-high heat, add the oil and shallots. Once the shallots begin to sizzle, reduce the heat to medium-low and cook, undisturbed, for 3-4 minutes or until you notice some of them taking on a light golden brown color. If they are burning too quickly, reduce the heat to low. Let them continue to sizzle, stirring and swirling the pan every 30 seconds so they cook evenly. Once they look almost done (a darker golden brown), stir in the peanuts and cook for another minute, stirring often. Turn off the heat.
Tilt the skillet and use a slotted spoon or spatula to transfer the shallots/peanuts to a paper towel lined plate or bowl. Sprinkle with salt and toss to coat. Pour the oil into a small heat-safe jar or bowl.
Serve the salad topped with the shallot/peanut topping (if using, or top with toasted nuts). Drizzle the reserved shallot oil over top (or just regular olive oil).