Blend to mix ingredients. Add two tablespoons of water and season to taste with salt and pepper. Blend again to mix. Add more water if you want a thinner consistency.
Immediately remove the asparagus from the water using a slotted spoon and plunge it into an ice water bath. Let it fully cool in the water, for about five minutes. When cooled, drain well.
Combine the diced tomato, hearts of palm, olives, and cooled asparagus in a bowl. Add the dressing and toss to lightly coat all the chopped ingredients with the dressing.