Step 1: In a large Dutch oven, melt 6 tablespoons of unsalted butter over medium heat until foamy but not browned.

Step 2: Add diced onion, carrots, and celery with a pinch of salt and black pepper. Increase the heat to medium-high and sauté for about 10 minutes, stirring occasionally, until the onion turns translucent and the carrots begin to soften.

Step 3: Reduce the heat to medium. Stir in the minced garlic, oregano, thyme, and sage. Cook for 1 minute, stirring often, until fragrant but not browned.

Step 4: Sprinkle the flour evenly over the vegetables. Stir constantly for 1 minute to create a roux and cook off the raw flour taste. The mixture will look slightly pasty—this is normal.

Step 5: Pour in a small splash of vegetable broth (about 2–3 tablespoons) to deglaze the pot. Scrape up any browned bits stuck to the bottom, as they will add flavor.

Step 6: Add the remaining broth along with the diced yellow potatoes, broccoli florets, and drained corn. Stir well to combine. Season with more salt and pepper to taste.

Step 7: Cover the pot and bring the soup to a gentle simmer over medium-high heat. Once simmering, reduce the heat to low and cook, covered, for 10–12 minutes, stirring once or twice, until the potatoes are fork-tender.

Step 8: Remove the pot from the heat. Stir in the heavy cream, then gradually add the shredded sharp cheddar cheese in small handfuls, stirring between each addition until melted and smooth. Finish with a teaspoon of balsamic vinegar to brighten the flavors.

Step 9: Taste and adjust seasoning with more salt and pepper if needed. If you’d like the soup thicker, lightly mash a few potato cubes against the side of the pot or let it sit for 5 minutes before serving. For a looser texture, add a splash of broth.

Step 10: Ladle into bowls and garnish with chopped parsley, extra cheese, and oyster crackers. Serve hot with crusty bread or a side salad.