Cook the rice according to the packet's instructions. Drain well.
In the meantime, prepare the rest of the dish. Chop the onions. Heat the oil in a large saucepan. Cook the onion until translucent, about 3-4 minutes.
Finely chop the garlic and the leeks, add to the pot and cook for another 2-3 minutes, stirring often.
Chop the peppers and the tomatoes. Add them to the pan and cook for another 2-3 minutes.
In a small bowl mix together all the ingredients for the BBQ sauce except the water. Add to the pan, stir in ¼ cup water, cover the pan and simmer for about 5 minutes, stirring a few times in between.
Check the pan. If the sauce seems dry, add the remaining ¼ cup water and stir well. Continue cooking for another 5 minutes or until the vegetables are soft and the sauce has thickened nicely without becoming dry.
Add the drained rice, stir well. Adjust the taste with salt, pepper, and, if necessary, with a pinch of sugar and/or more vinegar.
Garnish with chopped tomatoes, green onions, parsley, or chives, if desired.