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Coat the bottom of a large pot with olive oil and place it over medium heat. When the oil is hot, add the onion, carrots and fennel. Sweat the vegetables until they begin to soften a bit, about 10 minutes.
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Add the garlic to the pot and sauté it with the vegetables until it becomes very fragrant, about 1 minute.
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Add the wine, thyme, and oregano. Raise the heat and bring the wine to a simmer. Lower the heat and let the wine simmer until it has reduced by about half, which should take about 4 minutes.
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Stir in the broth, then raise heat to high. Bring the broth to a boil, then lower the heat and allow it to simmer, uncovered, for 10 minutes.
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Stir in the orzo. Continue to simmer the soup until the orzo is al dente, about 10 minutes.
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Stir in the spinach and let the soup continue simmering until the spinach has wilted and the pasta is tender, about 2 minutes.
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Remove the pot from heat and season the soup with salt and pepper to taste.
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Ladle the soup into bowls, then add a few meatballs to each bowl. Serve with a sprinkle of Parmesan cheese.