Mix achiote paste allspice, black pepper, oregano and vinegar. Roughly chop garlic, sprinkle with salt. Mix into a paste by blending with the back of a spoon. Add a little water if necessary until it is a thick spreadable paste. Add broth and heat to simmer.
Cut pork into 1 1/2 inch cubes place in a heavy-bottomed saucepan.
Cook uncovered until meat is browned evenly. Remove meat, pour off all but enough fat to coat bottom pan. Set aside.
Broil chile until blistered and blacken on all sides.
Cover with kitchen towel and let stand 5 minutes.
Peel pepper, cut out seed pod and dice.
Add rice and onion to pan with drippings.
Cook and stir until onion begins to brown. Add broth with spices, browned pork, chile, and carrots.
Stir once scraping rice from sides of the pan. Cook medium low for 15 minutes. Once rice is almost ready, stir in cooked peas, re-cover and let stand 5 to 10 minutes for rice to complete cooking. Salt to taste. Garnish with fresh cilantro and lime juice. This recipe is adapted from Rick Bayless' Mexican Kitchen recipe Achiote Rice Supper with Pork Carnitas
