Trim the chicken breasts and cut into uniform 1-inch cubes.
In a shallow bowl, whisk together the cornstarch, salt and pepper. Dredge the chicken pieces in the mixture to coat.
Over medium-high heat, heat the oil in large skillet. When hot, add chicken, tapping off excess cornstarch. Do not crowd the pan. Work in batches, if needed. Brown the chicken, approximately 5 minutes. Remove the chicken to a paper towel lined plate. Set aside. Repeat with the next batch if necessary.
Add 1 tablespoon of the vegetable oil and then add the broccoli florets, sauteing until they just start to soften and the ends get brown. Remove to a plate and set aside.
In same skillet (without cleaning it out or turning down heat), add the onions, garlic and ginger. If the pan is totally dry, add another 1-2 teaspoons of cooking oil. Saute for 2 minutes or until onions start to soften.
Stir in the coconut milk, chili garlic sauce, sugar, lime juice and lime zest and cilantro, cooking for another 3 minutes.
Return the cooked chicken and broccoli to the coconut sauce, tossing to coat. Cook over medium heat for an additional 2 minutes. Turn off the heat and allow to sit for 2-3 minutes before serving. The sauce will continue to thicken as the temperature decreases.
Spoon rice into a serving bowl, top with the chicken, broccoli and sauce. Garnish with fresh cilantro, lime wedges and a sprinkle of flaky sea salt.
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Notes
I sometimes add bottled roasted red peppers to give the dish more color. Just slice the peppers into strips and add in with chicken and broccoli to give them time to warm up.