Prepare the peas: If using dried peas, rinse them thoroughly and soak them in water for at least 4 hours, or overnight. Drain and rinse again before using. Canned peas can be used for convenience, just skip this step.
Sauté the aromatics: Heat olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Stir in the minced garlic and cook for an additional minute, until fragrant.
Add the flavor builders: Add the fresh thyme sprigs, diced tomatoes with their juices, vegetable broth, oregano, salt, and black pepper. Bring the mixture to a simmer.
Incorporate the rice and peas: Add the rinsed rice and drained pigeon peas to the pot. Stir gently to combine. Bring the pot back to a simmer, then reduce heat to low, cover, and cook for 18-20 minutes, or until the rice is fluffy and the peas are tender.
Fluff and serve: Remove the pot from the heat and let it sit for 5 minutes, covered. This allows the rice to steam and absorb any remaining liquid. Fluff the rice with a fork and discard the thyme sprigs. Garnish with chopped fresh cilantro, if desired.