In a large pot, melt 1 tablespoon of butter with olive oil over medium heat. Add diced carrots, celery, and onion. Sauté for 5–7 minutes until they begin to soften. Add the garlic and cook for 30 seconds, just until fragrant. The key here is not to rush the sauté, as this step builds the foundational flavor of the soup.

Stir in the chopped potatoes, Italian seasoning, salt, pepper, and chicken stock. Bring to a boil over medium-high heat, then reduce to a simmer. Cover and cook for 10–15 minutes, or until the veggies are crisp-tender. Stir in the thawed broccoli and frozen corn and cook for an additional 2–3 minutes, until everything is tender and heated through. The potatoes should be fork-tender for the best texture.

Meanwhile, in a separate medium saucepan, melt the remaining 4 tablespoons of butter over medium heat. Stir in the flour and whisk constantly for 1 minute. Slowly pour in the milk, whisking until the mixture is smooth. Continue to cook, stirring constantly, until it thickens and begins to gently boil. Stir in the heavy cream and remove from heat. This step creates a béchamel sauce that adds a creamy texture to your soup.

Pour the milk mixture into the soup pot and stir well to combine. Lower the heat, add the Cheddar cheese a handful at a time, and stir until melted. Taste and adjust the seasonings as needed. Adding the cheese slowly ensures it melts smoothly without becoming grainy.

Serve warm, garnished with fresh parsley or thyme, alongside toasted and buttered pieces of bread. Enjoy!