In a large pot, melt 1 tablespoon of butter with olive oil over medium heat. Add the diced carrots, celery, and onion, and sauté for about 5-7 minutes, allowing the vegetables to soften and release their flavors.

Add minced garlic and cook for an additional 30 seconds.

Stir in the chopped baby potatoes, Italian seasoning, salt, pepper, and chicken stock. Bring to a boil over medium-high heat.

Once boiling, reduce the heat to medium, cover the pot, and cook for 10-15 minutes until the vegetables are crisp-tender.

Add the thawed broccoli and frozen corn, stirring to combine. Cook for another 2-3 minutes until the vegetables are tender.

In a separate medium saucepan, melt the remaining 4 tablespoons of butter over medium heat. Gradually stir in the flour and whisk constantly for 1 minute to create a roux.

Slowly pour in the whole milk while whisking to avoid lumps. Cook until it thickens and reaches a gentle boil, then remove from heat and stir in the heavy cream.

Carefully pour the milk mixture into the vegetable soup and stir well to combine. Lower the heat again, and add the shredded Cheddar cheese a handful at a time, stirring until melted and smooth.

Taste the soup and adjust the seasonings as needed.

Serve the soup warm, garnished with fresh parsley or thyme, and alongside toasted and buttered bread.

Enjoy the comforting flavors and textures of your homemade creamy vegetable soup!