Begin by melting 2 tablespoons of butter in a large Dutch oven over medium heat. Once the butter is bubbly, add 1 diced white onion, 2 diced carrots, and 2 diced celery stalks to the pot. Sauté these vegetables for about 5-7 minutes, stirring occasionally, until they are soft and translucent.
Next, stir in 3 minced garlic cloves, 1 teaspoon of dried oregano, 1 teaspoon of dried thyme, and 1 teaspoon of dried sage. Cook this mixture for an additional 1-2 minutes until the garlic is fragrant.
Sprinkle in ¼ cup of flour, stirring well to combine everything into a smooth paste. Continue cooking for another 2 minutes.
Slowly pour in 4 cups of low-sodium vegetable broth while scraping the bottom of the pot. Bring the mixture to a gentle boil, then reduce the heat to a simmer.
Add 2 cups of chopped broccoli, 1 can of corn (drained), and 2 diced potatoes to the pot. Season with kosher salt and fresh cracked pepper to taste. Allow the soup to simmer for 10-12 minutes.
Once the potatoes are tender, stir in 1 cup of heavy cream and 1 cup of shredded sharp cheddar cheese. Continue to cook over low heat until the cheese melts completely.
Finally, ladle your creamy vegetable soup into bowls, garnishing with chopped parsley and extra cheddar if desired. Serve with crusty bread or crackers for dipping.