To prepare the squash, preheat the oven to 400°F. Spray a large baking pan with nonstick spray. Put the squash, cut side down, on the pan. Bake, turning once halfway through cooking time, until tender when pierced with the tip of a sharp knife, about 40 minutes. Remove from the oven and tent with aluminum foil to keep warm.

Meanwhile, to make the chicken, bring the chicken, water, onion, cilantro, garlic, salt, cumin, and bay leaves to a boil in a large saucepan over high heat. Reduce the heat to medium low and simmer, uncovered, turning the chicken occasionally, until the meat is opaque when pierced with the tip of a knife, 15 to 20 minutes. Transfer the chicken to a cutting board and let cool. Reserve 1½ cups of the cooking liquid. Discard the remaining cooking liquid and the solids. When the chicken is cool enough to handle, finely shred, using two forks to pull the meat apart. Transfer to a large bowl and set aside.

Spread the pumpkin seeds and peppercorns in a single layer in a large heavy skillet. Cook over medium heat, shaking the skillet frequently, until the seeds are toasted, fragrant, and slightly puffed, about 3 minutes. Transfer to a plate and set aside to cool. When cool, transfer the pumpkin seeds and peppercorns to a food processor and pulse until ground. Reserve 2 tablespoons of the mixture for garnish later.

Heat the oil in a large nonstick skillet over medium-high heat. Add the pumpkin seed mixture to the skillet and cook, stirring frequently, until the mixture just begins to brown, about 5 minutes. Slowly stir in the reserved cooking liquid and the salsa, and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, stirring occasionally, until the sauce begins to thicken, about 5 minutes. Stir in the shredded chicken and cook until heated through, about 2 minutes. For each serving, place a squash half on a dinner plate. Spoon the chicken mixture into each squash half, and sprinkle with the cilantro and reserved pumpkin seed mixture. Serve hot.