"Creamy, cheesy, Italian-y. Poaching the chicken breasts is easy, but any method of cooking is fine, including using leftovers! Serve hot, sprinkled with extra cheese if desired. So good with garlic bread."
Place chicken breasts in a large pot; cover with water. Bring to a boil; reduce heat and simmer until chicken is no longer pink in the center, 15 to 20 minutes. Drain and cool until easily handled, about 10 minutes. Cut into chunks.
Heat olive oil in a Dutch oven over medium heat. Add onion, shallot, and garlic; cook and stir until translucent and soft, but not browned, about 10 minutes. Stir in flour until combined.
Pour chicken broth into the Dutch oven. Add rosemary sprigs. Bring to a boil; reduce heat and simmer, covered, until flavors combine, about 20 minutes. Discard rosemary sprigs.
Whisk milk into the Dutch oven. Add fontina cheese in batches, whisking until each batch is melted. Stir in chicken chunks.