Heat oil over medium heat in a Dutch oven or a large heavy-bottomed pot with a lid. Add scallions and onions to pot and sprinkle with 1 teaspoon of salt. Sauté until onions are translucent, about 5 min. Stir in ½ teaspoon of thyme, cooking another minute.
Stir in black-eyed peas, making sure to coat them with oil. Add 5 cups of water and cover pot. Once at a boil, lower heat and simmer for about 45 minutes or until peas are tender but not mushy.
Pour in coconut milk and stir in Scotch Bonnet sauce or whole pepper, 1 teaspoon black pepper, 2 teaspoons salt and the rest of the water.
Season broth, adding salt or black pepper if needed. Stir in rice. Cover pot, [bring to a simmer then] reduce heat and let simmer for 25 to 30 minutes or until rice is tender but not mushy and liquid is absorbed. Check rice occasionally; add water if rice is too loose or remove cover to let liquid cook off if rice softens quickly.
Fluff rice and transfer to serving bowl. Garnish with the rest of the thyme.