In a medium skillet, heat 1 tsp. of the oil over medium-high heat. In a bowl, toss the hearts of palm with the remaining 1 tsp. oil and salt and pepper. Place them cut side down in the pan. If there's no sizzle, wait until the oil is hot; otherwise, they will not sear. When golden on one side, flip and repeat.
In a food processor, puree the dressing ingredients. In a large bowl, toss the olives, arugula, lettuce and avocado with the dressing. Arrange on a serving plate. Then cut the hearts of palm in half crosswise, so you can display the seared sides, and artfully place them around the outside of the plate.
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