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© Meredith Corporation. All rights reserved. Used with permission.
Heat oil in a large pot over medium heat. Add onion and garlic and cook, stirring occasionally, until softened, 2 to 3 minutes. Add oregano and marjoram; cook, stirring, for 1 minute. Add broth and chicken. Cover, increase heat to high and bring to a simmer. Uncover and cook, turning the chicken occasionally, until an instant-read thermometer inserted into the thickest part without touching bone registers 165°F, 20 to 22 minutes. Skim any foam from the surface as the chicken cooks. Transfer the chicken to a clean cutting board. When cool enough to handle, remove the meat from the bones and shred.
Meanwhile, add fennel, broccolini and tomatoes to the pot; return to a simmer. Cook until the vegetables are tender, 4 to 10 minutes. Stir in the shredded chicken, beans, salt and pepper and cook until heated through, about 3 minutes more. Remove from heat and stir in pesto.