Soak dried pigeon peas (or beans) overnight. Skip this step if using canned peas.
In a large pot, combine peas, salt beef (if using), onion, thyme, garlic, and bay leaves with 4 cups of water. Bring to a boil and simmer for about 20-30 minutes until the peas are soft (but not mushy). If using dry, unsoaked peas, cooking will take approximately 1 hour.
Remove the thyme, garlic, and bay leaves. If the liquid is running low, top up with the remaining 2 cups of water. Add the rinsed rice and the diced tomato. Season with salt and pepper to taste.
Increase heat to a rolling boil, then immediately reduce to minimum, cover tightly, and simmer for 20-25 minutes without stirring. The rice should absorb all the liquid during this time.
Turn off the heat and let the rice sit, covered, for 10 minutes. This finishes the cooking and keeps the rice fluffy.
Uncover and gently fluff the rice with a fork. Serve hot as a side dish to any Caribbean stew or fish.