In a large pot over medium heat, melt 1 tablespoon of the butter and add the olive oil. Add diced onion, carrots, celery, and bell pepper and sauté 7–9 minutes. Add garlic and sauté 30 seconds more.
In a separate pot, cook tortellini according to package directions (see note 2). Drain and set aside. (Salt the pasta water once boiling; I add in 1 teaspoon salt to every 4 cups of water.)
Add the seasonings to the pot with the veggies—dried thyme, dried oregano, Italian seasoning, and cayenne pepper (if using). Season to taste with salt and pepper. (I add 1 teaspoon salt and 1/2 teaspoon pepper, but add to preference.) Stir seasonings for 30 seconds.
Increase heat to medium-high. Push veggies to the sides of the pot and add the remaining 4 tablespoon butter to the center and stir until melted. Once melted, sprinkle in the flour. Briskly mix to incorporate the flour and stir for 1 minute to cook off the raw flour. Gradually whisk in 1 cup of chicken broth until it starts to thicken (1 minute); then add the remaining chicken broth. Whisk until it thickens (2–3 minutes), then gradually add the milk, stirring constantly. Slightly reduce the heat and cook, continuing to stir, until mixture begins to gently boil and thicken, another 2–5 minutes.
Reduce heat to medium low. Add the frozen corn and chicken. Stir to warm through. (If the soup has thickened too much, add some additional chicken stock; I usually add 1/2 cup to 1 cup extra).
Remove pot from heat and add the cheese. Stir to melt. Season soup to taste with any additional salt and pepper. Add parsley (if using). Serve, adding tortellini to individual bowls. Garnish with fresh thyme and serve with crusty bread if desired.
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Notes
Note 1: I recommend good quality tortellini. If you have a favorite tortellini, use that; otherwise, there are some taste-tested recommendations here and here!Note 2: It’s best to cook the tortellini separately from the soup. Different types of tortellini require different cook times, making it tricky to get right in the soup. Plus, leftover tortellini can absorb too much liquid and turn mushy. Cooking it on the side is also quicker—ready just as the soup finishes!Storage: Store leftovers in an airtight container in the fridge for up to 3 days. The tortellini will absorb liquid, so add a splash of broth when reheating. Freezing isn’t recommended since the pasta can get mushy.