Blend all vinaigrette ingredients until emulsified; store tightly covered in the refrigerator until ready to serve
Cover the split peas with 1-inch of boiling water and let soak for 1 1/2 hours. Drain well, spread on a paper towel lined baking sheet and blot to dry. Heat oil to 350˚F in a small skillet or saucepan and line another sheet pan with paper towels. Fry the peas for 3 minutes or until crispy and starting to brown. Quickly remove from oil and drain on paper towels; season with salt. (May be prepared a day ahead and stored in an airtight container.) Drop shallots into hot oil and cook just until golden brown. Remove and drain on paper towels.
Toss all of the salad ingredients together in a large bowl. Drizzle with vinaigrette just before serving and toss well to coat. Top with the fried peas and shallots and garnish with lime wedges, if desired. Makes 4 servings.