Using a meat mallet, pound chicken to about ½ inch thick evenly (this helps with even cooking). Season each chicken breast with ½ teaspoon Italian seasoning, ½ teaspoon garlic powder, ½ teaspoon Kosher salt and ¼ teaspoon ground black pepper.
Heat about 2 tablespoons of olive oil in a large skillet over medium heat. Cook the chicken, about 6 minutes per side, or until internal temperature reaches 165 degrees F. Set aside and let it rest for at least 10 minutes.
Meanwhile, in a large 6-quart Dutch oven or pot, melt the butter over medium heat. Sauté celery, carrots, onions, and celery until softened, about 6 minutes, stirring occasionally. Then add the minced garlic and thyme, and cook for another 1 to 2 minutes until fragrant.
Stir in the all-purpose flour to coat the vegetables. Gradually add the chicken broth, stirring to dissolve and break up any lumps. Bring to a boil, and then reduce to simmer. Simmer for about 5 minutes, partially covered, until slightly thickened.
Stir in the half-and-half and let it return to a simmer. Then, add the gnocchi and cook for 5 to 6 minutes, uncovered, until cooked through and pillowy soft. If needed, add more broth or half-and-half to taste.
Shred or dice the cooked chicken, and add it into the soup. At this point, season with salt and pepper to taste.
To finish, stir in the baby spinach and cook for another minute until reduced. To serve, garnish with freshly grated parmesan cheese and freshly ground black pepper. Enjoy!