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In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic and sauté until they become translucent.
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Add the diced carrots and celery and cook for about 5 minutes until they begin to soften.
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Stir in the flour to make a roux. Cook for a few minutes until the mixture turns a light golden brown.
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Slowly whisk in the chicken broth and milk to create a smooth sauce.
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Add the cooked chicken, frozen peas, frozen corn, dried thyme, salt, and pepper. Stir and simmer for a few minutes until the filling thickens. Remove it from the heat.