In a saucepan large enough to hold the 3 cups of water (or broth) and achiote paste, mix the achiote powder with the allspice, pepper, oregano and vinegar.
Finely chop the garlic and then sprinkle it with the salt.
Using the back of a spoon or the edge of your knife, grind the garlic and salt into a paste on your cutting board. Add to the spice and vinegar mixture in the saucepan.
Combine your chosen vegetables in one or more bowls, with the vegetables divided up by the amount of time they will need to reheat in the finished dish (e.g., cooked squash in one bowl, defrosted corn or peas in one bowl, fully cooked poblano chilies and raw tomatoes in another). Set aside.
In a medium saucepan (2 quarts or larger), heat the cooking oil.
Add the rice and cook, stirring constantly, until the rice is coated with oil and has a chalky look in places, about 30 seconds to 1 minute.
Adapted from Rick Bayless's Mexican Kitchen