Heat a large stockpot over medium heat and add the butter.

When the butter is melted, stir in the diced carrot, chopped celery, and chopped onion. Cook until the vegetables are tender, about 5 minutes, then add the minced garlic and cook one minute more.

Stir in the diced potatoes, chicken broth, Italian seasoning, and bay leaf. Bring the liquid to a boil, then reduce the heat to low and simmer for 20 minutes, until the potatoes are tender.

While that simmers, whisk together the milk, heavy cream, and cornstarch in a small bowl until completely smooth with no lumps.

Remove the bay leaf from the pot, then stir in the milk mixture along with the broccoli florets and corn.

Let the soup simmer for 10 minutes, until the broccoli is tender and the soup has thickened.

Season with salt and pepper before serving.