Stir together the coconut milk, 2 cups water, 5 to 6 sprigs cilantro, red pepper flakes, garlic, ginger, 2 lime halves, half of the sliced red onion, 1 tablespoon salt and a couple grinds of black pepper in a large, deep skillet or saute pan over medium heat.

Place the chicken breasts in the coconut mixture, making sure they are completely submerged. Bring the liquid to a boil, then immediately lower the heat to maintain a gentle simmer. Continue cooking until the chicken reaches an internal temperature of 160 to 165 degrees F when measured with an instant-read thermometer in the thickest part, 25 to 27 minutes. (Start checking the temperature after 20 minutes to make sure the chicken does not overcook.)

Remove the chicken from the poaching liquid and place on a cutting board. Bring the remaining liquid to a boil and cook to thicken, about 5 minutes. Strain the poaching liquid through a fine-mesh sieve into a clean saucepan and keep warm.

Slice the chicken breasts into ¼-inch thick pieces.

To plate, put 1 cup cooked white rice in a wide bowl, place 1 sliced chicken breast next to the rice and spoon some of the coconut sauce on top. Top the chicken with the sliced radishes in a shingled pattern. Garnish each bowl with the nuts and remaining cilantro, sliced red onion and lime wedges. Drizzle with extra-virgin olive oil and serve with sweet chili sauce.