Mash the avocados, lemon zest, lemon juice, sugar, and parsley together in a bowl. Set aside.
Heat the olive oil in a skillet over medium-low heat; cook the garlic in the hot oil until slightly browned, about 5 minutes. Add the prawns and increase heat to medium. Season with salt and pepper. Cook and stir the prawns over medium heat until they begin to change color. Reduce heat to low. Stir the avocado mixture into the prawns; cook until the avocado is completely heated, about 2 minutes. Garnish with a little bit of black pepper to serve.