Set a medium saucepan over medium heat. Put the rinsed rice, the coconut milk, 2/3 cup water, and 1/2 teaspoon of the salt into the saucepan.

Bring the liquid to a gentle boil, stirring once so the rice does not stick to the bottom of the pan.

Cover the saucepan, turn the heat to low, and cook for 15 minutes. The rice is ready when the liquid is absorbed and the grains are tender.

Take the saucepan off the heat and leave it covered for 5 minutes so the rice can finish steaming.

While the rice cooks, put half of the sliced red onion into a medium bowl. Add the juice from 1 lime and 1/4 teaspoon of the salt, toss well, and set the bowl aside to soften and lightly pickle.

Put the drained black-eyed peas into a colander if you have not already, and let any extra water drip off.

Set a large skillet over medium heat. Add 1 tablespoon of the oil to the skillet.

Put the remaining sliced red onion and the bell pepper into the skillet. Cook for 6 to 8 minutes, stirring now and then, until the vegetables are soft and starting to brown at the edges.

Add the chopped garlic and cumin to the skillet. Stir for 30 seconds, just until the garlic smells fragrant.

Add the black-eyed peas to the skillet with the vegetables. Sprinkle in the remaining 1/2 teaspoon salt and the black pepper, then stir in 1/4 cup water.

Cook the bean mixture for 3 to 4 minutes, stirring once or twice, until the beans are hot and the small amount of liquid has mostly cooked away. Turn the heat to low to keep the beans warm.

Set a second large skillet, preferably nonstick, over medium heat. Add the remaining 2 tablespoons oil to the skillet.