Cover the split peas with 1-inch of water and let soak for 1 hour. Drain well, spread on a paper towel lined sheet pan, and blot to dry. Heat the oil to 350˚F in a deep-fryer or wide deep pot and line another sheet pan with paper towels. Fry the peas until crispy, 4 to 5 minutes, drain briefly on the paper towels, and sprinkle with salt. The peas can be made a day ahead and stored in an airtight container.
Blend all of the vinaigrette ingredients in a nonreactive container with an immersion blender until emulsified.
To serve: Toss all of the salad ingredients together in a large bowl and divide between individual bowls or arrange on a large platter. Just before serving, drizzle with the vinaigrette and top with the fried peas. Garnish with lime wedge(s), if using.
*Ingredients available at Asian grocery stores and through specialty food distributors.