Melt 2 tablespoons of unsalted butter or heat olive oil in a large pot over medium heat. Add 1 diced onion and 2 minced garlic cloves, stirring frequently for 3–4 minutes until translucent.

Stir in 2 cups of diced carrots and potatoes, cooking for an additional 5 minutes to soften.

Sprinkle 1/4 cup of all-purpose flour over the vegetables and stir to coat evenly. Cook for about 2 minutes.

Gradually whisk in 4 cups of vegetable broth. Stir until thickened slightly, about 3 minutes.

Add 1 teaspoon each of dried thyme and rosemary, along with salt and pepper to taste. Simmer for about 15 minutes.

Stir in 1 cup each of broccoli florets, frozen peas, and corn kernels. Simmer for an additional 5–7 minutes.

Lower the heat and stir in 1 cup of whole milk and optional heavy cream. Adjust seasonings if needed.

Ladle the soup into bowls and garnish with freshly chopped parsley. Serve immediately with bread or salad.