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. Add garlic and cook for 30 seconds.

Stir in chopped potatoes, Italian seasoning, salt, pepper, and chicken stock. Bring to a boil over medium-high heat, then reduce to medium. Cover and cook for 10–15 minutes, or until the veggies are crisp-tender. Stir in thawed broccoli and frozen corn. Cook for 2–3 more minutes, until tender and heated through.

Meanwhile, in a medium saucepan, melt 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 smooth. Cook, stirring constantly, until thickened and gently boiling. Stir in the heavy cream and remove from heat.

Pour the milk mixture into the soup and stir well. Lower the heat, add Cheddar cheese a handful at a time, and stir until melted. Taste and adjust the seasonings as needed.

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