Arrange the chicken: Place the chicken breasts in a single layer in a 4- to 5-quart saucepan or Dutch oven. If the breasts are unusually thick, cut them horizontally into thinner pieces so they cook more evenly.

Add the aromatics: Add the quartered onion, crushed garlic, salt, black pepper, oregano, and bay leaf.

Add the broth: Pour in the chicken broth: The liquid should mostly cover the chicken. If necessary, add a small amount of water to bring the liquid level just over the thickest pieces.

Bring to a gentle simmer: Place the pan over medium-high heat and bring the broth just to a simmer. Small bubbles should rise steadily around the edges, but the liquid should not boil aggressively.

Cook gently: Reduce the heat to low or medium-low and partially cover the pan. Simmer gently for 12 to 18 minutes, depending on the thickness of the chicken.

Check for doneness: Insert an instant-read thermometer into the thickest part of the largest chicken breast. The chicken is done when it reaches 165°F (74°C). The center should be opaque with no translucent areas.

Remove the chicken: Transfer the cooked chicken to a clean cutting board or shallow bowl using tongs.

Rest the meat: Let the chicken rest for 5 minutes before shredding. This short rest allows the juices to settle inside the meat.

Reserve some cooking liquid: Strain about 1 cup (240 ml) of the cooking broth through a fine-mesh strainer. Discard the onion, garlic, and bay leaf.

Shred the chicken: Use two forks to pull the warm chicken into thin strands. For chunkier shredded chicken, stop once the meat separates into bite-size pieces.

Moisten the chicken: Add 1/4 cup (60 ml) of the reserved cooking liquid to the shredded chicken and toss gently. Add another tablespoon or two if the chicken still looks dry.

Taste and serve