Heat a large skillet over medium-high heat. Cook and stir chorizo in the hot skillet until browned and crumbly, 5 to 7 minutes. Drain and discard grease.

Add tomatoes, onion, carrot, celery, garlic, Worcestershire sauce, adobo, basil, and cilantro to the skillet with the chorizo. Simmer for 5 minutes. Add rice and simmer for 5 minutes more. Remove from heat, add fresh parsley, and let rest.

Preheat the oven to 350 degrees F (175 degrees C). Spray a baking dish with cooking spray.

Stuff each poblano pepper half with the chorizo mixture; lay in the baking dish. Add water to the bottom of the dish. Loosely cover with aluminum foil.

Bake in the preheated oven until peppers are tender but still firm, about 1 hour. Remove foil and sprinkle peppers with Cheddar, mozzarella, and pepper Jack cheeses.

Turn on the broiler; broil peppers until cheese is brown and bubbly, 3 to 4 minutes.