Heat the olive oil in a large Dutch oven over medium heat. Add the onion, bell pepper, celery and 1/2 teaspoon salt; cook 6 minutes, stirring, until softened.
Add the garlic, smoked paprika and thyme; cook 30 seconds until fragrant.
Stir in the rice and 2 1/2 cups water. Bring to a boil, cover, reduce the heat to low and simmer 20 minutes.
Scatter the collard greens over the rice without stirring, cover and cook 15 minutes, until the rice is tender and the greens are soft.
Fold in the black-eyed peas and cook 5 minutes more; add 2-4 tablespoons water if the pot looks dry.
Turn off the heat, stir in the vinegar, season with salt and pepper, and rest 5 minutes before fluffing and serving.