Season the Chicken: Rub the chicken breasts with 1 teaspoon of kosher salt and let them sit while you prepare the other components.
Prep the Vegetables: Slice the ears of corn into 1½-inch-thick rounds. Separate the cilantro stems from the leaves, chopping both coarsely but keeping them separate. For the onion, slice two-thirds into thick rounds and finely dice the rest, aiming for about ½ cup of diced onion.
Char the Onion: Heat a dry skillet over medium-high heat. Lay the thick onion slices in the pan and cook them without moving until one side is browned, about 3 to 5 minutes. Flip and brown the other side, then remove the onions from the pan.
Make the Broth: Add the cilantro stems, oregano, garlic cloves, bay leaf, and sliced jalapeño to the skillet along with the charred onion slices. Pour in the chicken stock and 1 cup of water, then season with 1 teaspoon of kosher salt. Bring this mixture to a gentle simmer and let it cook for about 15 minutes to infuse the flavors.
Cook the Chicken and Corn: Add the seasoned chicken breasts to the simmering broth. Cover the skillet and reduce the heat to low, letting the chicken poach until fully cooked, about 7 to 10 minutes. Add the corn rounds to the skillet during the last 3 minutes of cooking.
Prepare the Garnish: While the chicken is cooking, mix the reserved diced onion, chopped cilantro leaves, diced tomato, lime zest, lime juice, and the remaining ½ teaspoon of kosher salt in a small bowl. This mixture will serve as a fresh garnish.
Assemble the Dish: Remove the chicken and corn from the skillet, transferring them to a cutting board. Strain the broth into serving bowls, discarding the herbs and aromatics. Slice the chicken and divide it among the bowls, along with the corn.
Finish and Serve: Top each bowl with a generous spoonful of the prepared garnish. Add diced avocado, a dollop of salsa, and a sprinkle of capers (if using). Finish with a squeeze of fresh lime juice before serving.