Heat a cast-iron skillet or frying pan over medium-high heat. Add imitation bacon in a single layer. Cook about three minutes, until lightly browned. Flip over and cook until crispy. Remove from the skillet and drain on paper towels. If some oil is left in the skillet, skim off one tablespoon to use in the dressing (if you like). Chop cooled imitation bacon into 1/4-inch pieces and set aside.

Remove yolks from three of the hard-boiled eggs. Chop the whites and reserve for the salad. Reserve the fourth hard-boiled egg as a salad topper.

In a container with a tight-fitting lid, mix three hard-boiled yolks, mustard, sugar, basil, red wine vinegar, oil from cooking the imitation bacon, olive oil, salt, and pepper. Seal and shake vigorously until well blended. Set aside.

Place lettuce on a platter or in a bowl. Toss with a small amount of dressing. Add imitation bacon, chicken, tomatoes, chopped egg whites (from step 2), avocado, and jicama. Drizzle with more dressing. Serve immediately, topped with the last hard-boiled egg and with extra dressing on the side.