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In a stockpot, heat the olive oil over medium heat until it runs quickly through the pan.
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Add the chopped onion, carrots and thyme.
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Cook until the onion is translucent and carrots are slightly tender, stirring often, about 4-5 minutes.
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Stir in the garlic and cook, stirring constantly, until fragrant.
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Whisk in the flour and cook, whisking or stirring constantly, until the flour is lightly golden, 1-2 minutes.
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Slowly whisk in the milk.
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Whisk in the milk and chicken broth.
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Stir while bringing the mixture to a boil over medium to medium-high heat.
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Cook, stirring often, until the mixture is slightly thickened, 5-7 minutes.
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Stir in the uncooked gnocchi and simmer over medium-low heat for 3-4 minutes, stirring occasionally. The soup should thicken up quite a bit while the gnocchi is cooking.
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Stir in the chicken and spinach and cook for 1-2 minutes until heated through.
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Season with salt and pepper to taste and serve.