Cut 1 onion in half. Place onion halves, stock, chicken breasts, carrots, 5 cilantro stems, and 2 serrano chiles in a large Dutch oven; press down on chicken to fully submerge. Bring to a boil over medium-high. Remove from heat; cover and let stand until a thermometer inserted in thickest part of chicken registers 150°F, about 20 minutes.

Meanwhile, cook poblano chile in a medium cast-iron skillet over medium-high, turning occasionally, until all sides are blackened, 4 to 6 minutes. Transfer charred poblano to a medium bowl; cover with a plate, and let stand 15 minutes. Carefully peel poblano under running water; discard skin, stem, and seeds. Set poblano flesh aside.

Cook cumin, coriander, anise seeds, peppercorns, cinnamon stick, and cloves in a medium skillet over medium-low, stirring often, until toasted and fragrant, 1 to 2 minutes. Transfer to a molcajete or spice grinder; process until finely ground. Set aside.

Remove and discard vegetables and cilantro stems from chicken mixture. Using tongs, transfer chicken to a large saucepan or heatproof bowl with a tight-fitting lid. Add ½ cup cooking liquid from Dutch oven to chicken; cover and set aside. Transfer remaining cooking liquid to an 8-cup measuring cup or a large bowl; set aside. Wipe Dutch oven clean.

Roughly chop remaining 2 onions. Remove and discard stems and seeds from remaining 4 serrano chiles; chop serranos. Heat oil in a large skillet over medium. Add onions, serranos, tomatillos, and garlic; cook, stirring occasionally, until softened but not browned, 12 to 14 minutes. Remove from heat; transfer mixture to a blender, and add 2 cups reserved cooking liquid. Secure lid on blender, and remove center piece to allow steam to escape. Place a towel over opening. Process until smooth, about 30 seconds. Transfer mixture to cleaned Dutch oven over medium-low. Stir in ¾ cup duck fat.

Place radish greens, spinach, parsley stems, epazote stems, poblano flesh, 2 ½ cups reserved cooking liquid, and remaining cilantro stems in blender. Process until smooth, about 45 seconds. Add to onion mixture in Dutch oven.

In a clean blender, process pepitas, almonds, sesame seeds, and remaining reserved cooking liquid until mixture forms a loose, coarse paste, 25 to 35 seconds. Add pepita mixture, reserved spice mixture, and salt to Dutch oven. Bring to a boil over medium-high; reduce heat to medium-low, and cook, stirring often, until mixture thickens and reduces slightly, about 1 hour. Stir in remaining ¾ cup duck fat; cook over medium-low, stirring often, until a thin layer of fat forms on top, 20 to 30 minutes.

Meanwhile, remove and discard skin and bones from chicken. Shred chicken still in juices in saucepan; toss with juices. Add chicken mixture with juices to mole; cook, stirring often, until chicken is heated through, about 5 minutes. Season with salt to taste. Garnish with additional toasted sesame seeds, reserved cilantro leaves, and onion rings. Serve mole hot with tortillas.