In a large stock pot, melt butter. Add onions, celery and garlic. Saute until onions are tender and translucent.
Add flour and whisk to combine. Whisk in about a cup of chicken broth. Gradually add the remaining chicken broth. Continue to whisk and simmer over medium heat until broth thickens. Add half and half return to simmer.
Add chicken, grated carrots, chopped spinach, gnocchi and seasonings. Bring to a boil then reduce heat to a simmer. Simmer for about ten minutes.
Add cheddar cheese. Stir until melted. Serve warm!