Heat the oil in a dutch oven or soup pot to medium heat. Add the onions and garlic and stir to coat. Cook for 3-5 minutes until the onions are softened. Add the broth and water and increase the heat to bring the contents to a boil. Add the chicken breasts, carrots, celery, rosemary, thyme and nutmeg and once bubbling again, reduce the heat to a simmer and cover. Simmer, covered, for 25-30 minutes until the chicken breasts are cooked through and the vegetables are tender.
About 10 minutes before the chicken is done simmering, mix together the flour, salt and pepper in a small dish. Melt the butter in a medium saucepan over medium heat. Slowly whisk in the flour a little at a time until fully combined and let the “paste” that forms cook for 1-2 minutes. Slowly whisk in the half-and-half a little at a time until the mixture is completely combined, smooth and creamy. Cook for another few minutes, whisking occasionally, until the mixture thickens and lightly bubbles. Remove from heat.
When the chicken from step one is finished cooking, remove it to a cutting board (recover the pot and continue to simmer the other ingredients). Chop the chicken into bite-sized pieces and set aside.
Uncover the simmering pot and add the gnocchi to the broth and vegetables. Re-cover and simmer for the time listed on the package of gnocchi (likely somewhere between 2-5 minutes). Uncover and whisk or stir in the creamy mixture from step two until well combined. Add the chopped chicken and the spinach to the pot and stir to combine. Cook, stirring, for another 2-3 minutes until spinach is wilted. Add salt and pepper to taste if desired. Serve warm.