Step 1

Use a vegetable peeler to remove four 2-inch strips of lime zest and two 2-inch strips of grapefruit zest. Juice limes and grapefruit, setting aside 2 tablespoons of each juice. (Reserve remaining juice for another purpose.) Set aside zests and juice.

Step 2

For the Broth: Split onion in half from pole to pole and set one half aside. Place other half in a large saucepan. Add chicken or turkey, 4 garlic cloves, bay leaves, cloves, cinnamon, allspice, peppercorns, and oregano. Add chicken broth and top up with water until all ingredients are submerged. Heat over medium heat until gently simmering. Reduce heat until broth is steaming-hot, but not bubbling. Cook, turning chicken occasionally, until center of chicken registers 150°F on an instant-read thermometer, about 30 minutes. Remove from heat.

Step 3

Using tongs, carefully remove chicken from broth and transfer to a bowl. Strain broth through a fine-mesh strainer into a heatproof container and add lime zests and grapefruit zests. (There should be at least 1 quart of broth; if not, adjust with water.) Set aside to steep.

Step 4

Meanwhile, for the Sofrito: Thread remaining 4 garlic cloves onto a metal skewer and roast over the direct heat of a gas flame, turning, until garlic is charred on all surfaces, about 3 minutes total. Set aside. Using tongs, roast tomatoes over the flame until their skins bubble and peel back, about 30 seconds. Alternatively, roast garlic in a dry skillet over medium-high heat, tossing constantly, until charred on most surfaces. Remove garlic and add tomatoes and roast, turning constantly, until blistered all over.

Step 5

Peel garlic and tomatoes and discard skins. Finely mince both. Finely mince remaining onion half. Heat 2 tablespoons (30ml) vegetable oil in a large saucepan over medium heat. Add garlic, tomatoes, pepper, and minced onion, season with a pinch of salt, and cook, stirring frequently, until sofrito is completely softened but not browned, about 10 minutes.

Step 6

Remove lime and grapefruit zests from broth and discard. Pour broth into pot with sofrito. Add reserved lime and grapefruit juice and season broth to taste with salt.

Step 7

For the Tortilla Strips: Combine remaining 1/4 cup (60ml) oil and tortilla strips in a nonstick or cast iron skillet. Heat over medium heat, stirring and tossing frequently, until tortilla strips are mostly crisp all over, about 3 minutes. Transfer tortilla strips to a paper towel–lined plate to drain.

Step 8

To Serve: Shred chicken or turkey meat into bite-size strips with your fingers or two forks. Discard bones and skin. Divide meat evenly between serving bowls and top with hot broth. Add a small handful of tortilla strips and sprinkle with cilantro. Cut half of final lime into wheels and remaining half into wedges. Add lime wheels to soup and serve immediately with wedges on the side.