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Step 1
Place 4 skin-on, bone-in chicken breasts (3–4 lb.) in a large bowl or resealable plastic bag. Finely grate 2 large oranges and 2 limes into a food processor or blender with a Microplane. Cut zested oranges and limes in half and squeeze juice into processor (you should get about 1¼ cups juice). Cut 1 medium onion into quarters, then add it to processor along with 6 garlic cloves. Add 1 Tbsp. vegetable oil or grapeseed oil, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, 1 Tbsp. ancho chile powder, 2 tsp. ground cumin, 1 tsp. dried Mexican oregano, and 1 tsp. freshly ground black pepper and process or blend until slightly chunky but uniform in color. Pour over chicken and toss to evenly distribute. Cover bowl (or seal bag) and chill at least 30 minutes and up to 4 hours.
Step 2
Meanwhile, prep the salsa ingredients. Remove husks from 1 lb. tomatillos; discard. Rinse tomatillos and place in a medium heatproof bowl. Peel remaining 1 medium onion, cut in half, and add to bowl. Remove stems from 2 jalapeños or serrano chiles; discard. Add chiles to bowl. Drizzle in 1 Tbsp. vegetable oil or grapeseed oil and add remaining 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt; toss to coat.
Step 3
Fill a chimney starter with charcoal and lightly pack crumpled newspaper or brown paper bags into the bottom of the starter. Remove upper grate from grill and place chimney starter on lower grate. Using a lighter or long match, light newspaper. As the paper burns the coals will slowly ignite. After 10–15 minutes, coals should be glowing and coated in white ash with little to no black spots remaining. Carefully dump coals onto half of grill in an even layer. If needed, use a long pair of grill tongs to push coals into place. Coat upper grate with oil and set over coals. Your grill is now prepared for 2-zone heat—the side with coals is the hot zone and the side without coals is the cool zone. Cover grill and open air vent on top. Let heat 5 minutes.
Step 4
Remove chicken from marinade, allowing excess to drip back into bowl; discard marinade. Place chicken, skin side up, on grate over indirect heat. Cover, making sure air vent is over chicken, and grill until an instant-read thermometer inserted into thickest part of a breast registers 155°, 25–30 minutes.
Step 5
Uncover grill and slide chicken breasts over direct heat. Grill, still skin side up, until crisp and lightly charred in some spots underneath, about 2 minutes. Turn over and grill on other side until crisp, deep golden brown, and charred in some spots, about 2 minutes. Check internal temperature again—thermometer should register 160°. If not, move chicken back over indirect heat, cover, and let cook another 2–4 minutes before checking temperature one last time. Transfer chicken to a platter and let rest in a warm spot 15 minutes.
Step 6
While the chicken rests, make the salsa. Arrange tomatillos, onion, and chiles on grate over direct heat. Cook, turning occasionally, until vegetables are softened and lightly charred all over and tomatillos release their juices, 10–12 minutes. Transfer vegetables back to bowl and let cool slightly.
Step 7
Arrange tortillas over direct heat and grill until warmed through, pliable, and lightly charred in spots, about 30 seconds on each side. Wrap tortillas in a kitchen towel to keep warm.
Step 8
Transfer tomatillos, onion, and chiles to clean food processor or blender and add remaining 1 garlic clove and ¼ cup cilantro leaves with tender stems. Cut remaining 1 lime in half and squeeze juice into processor. Cover and pulse until salsa is thick and chunky but pourable. Transfer to a bowl. Serve salsa with chicken, warm tortillas, and more cilantro. (You can pull meat from the bones and slice and shred before serving, if desired; discard bones.)