Toss pork with 1/4 teaspoon salt and pepper. Heat oil in a large nonstick skillet over medium heat. Add the pork and cook, stirring, until just cooked through, 4-6 minutes. Transfer to a bowl with a slotted spoon.
Add onion, tomato paste and rice to the pan and cook until the onion softens, about 4 minutes. Add kale and garlic and cook until the kale begins to wilt, 1-2 minutes. Stir in broth, vinegar, paprika and the remaining 1/4 teaspoon salt. Bring to a boil. Cover, reduce heat and simmer until the rice is done, 15-20 minutes. Stir in the reserved pork and black-eyed peas and heat for 1 minute.