Heat a medium heavy-bottomed saucepot or Dutch oven over medium-high heat. Add the black-eyed peas and cover with cold water by 1 inch (should be about 6 cups water). Add the smoked turkey and a pinch of salt and bring to a boil. Reduce to a simmer and cook over medium heat, covered, until tender, about 2 hours, then turn off the heat.
Melt the butter and oil in a large saucepot over medium-high heat. Add the onions and peppers. Season with salt and pepper and cook just until slightly softened, about 5 minutes. Add the garlic and cook 1 minute more. Add the rice to the pot and stir until toasted, about 5 minutes.
Add 3 cups water and 1 cup of the cooking liquid from the peas. Bring to a boil, then cover and cook over medium-low heat until the rice is tender and cooked through, 15 to 20 minutes. Fluff the rice with a fork and gently stir in 2 cups of the cooked peas (save the remainder for another use). Cover and cook for 10 minutes more. Transfer to a serving bowl and top with the sliced scallions before serving.
Use the rest of the peas for another use, or reduce the peas and meat by half when cooking.