In a large pot, melt 2 tablespoons of unsalted butter or olive oil over medium heat. Add diced onions and minced garlic, stirring occasionally for about 3–4 minutes until they become fragrant and translucent.

Toss in the diced carrots and potatoes, stir to mix with the aromatics. Sauté for about 5 minutes.

Sprinkle 1/4 cup of all-purpose flour over the sautéed vegetables. Cook for an additional 1–2 minutes, stirring constantly.

Gradually whisk in 4 cups of vegetable broth, stir continuously to avoid lumps, and bring to a gentle boil.

Season with 1 teaspoon of dried thyme, 1/2 teaspoon of dried rosemary, and salt and pepper to taste. Reduce heat and let simmer uncovered for about 15 minutes.

Stir in the broccoli florets, frozen peas, and corn kernels. Simmer for another 5–7 minutes.

Lower heat and mix in 1 cup of whole milk or half-and-half and 1/2 cup of heavy cream, stirring until thickened.

Ladle into bowls and garnish with fresh parsley.