In a large heavy pot or Dutch oven, melt the butter (2 tablespoons) over medium-high heat. Add the diced onion (1), diced carrots (2), diced celery (2 ribs), the thyme (1 teaspoon), and the oregano (1 teaspoon). Stir to coat in the butter and sauté until vegetables are softened and browned, stirring occasionally, about 5 minutes.
Add the minced garlic (2 cloves), stir, and sauté until fragrant (about 15-30 seconds).
Add the flour (1/4 cup) and stir to coat the veggies. Cook for about 1 minute, stirring frequently.
Pour in the chicken broth (4 cups) and stir to scrape up any stuck-on bits on the bottom and make sure all the flour is dissolved. Bring to a gentle boil.
Add the gnocchi (16 oz.) and simmer uncovered for about 3 minutes, until gnocchi are cooked and start to float to the top.
Stir in the cooked chicken (2 cups), chopped fresh spinach (2 cups), half and half (1 cup), and grated parmesan (3/4 cup). Continue heating and stirring frequently until spinach is wilted, cheese is melted, and chicken is heated through (about 3 minutes).
Season with kosher salt and black pepper to taste. Serve.
For a gluten-free version, make sure to use gluten-free flour and gluten-free gnocchi.
For a lower-carb version, use cauliflower gnocchi and skip the all-purpose flour/roux step (the soup will be thinner).
For a lighter version, use milk instead of half and half, 1/2 cup of parmesan, and chicken breast meat.
Because this soup cooks so fast, the celery, carrots, and onions may be a bit crunchy. If you prefer softer veggies, sauté them for longer, or really finely dice the onion and celery and grate the carrots.