Heat the oil in a large soup pot over medium-low heat. Add the diced onion, celery, carrots and sauté for about 4 minutes, until softened and fragrant. Stir in the garlic and cook for 30 seconds.
¼ cup olive oil, 1 medium onion, diced, 3 stalks celery, chopped, 2 medium carrots, peeled and chopped, 3 cloves garlic, minced
Add the flour with the vegetables and cook for 2 minutes, stirring often, to lightly toast it.
¼ cup flour
Add the dried oregano, dried basil, salt, and pepper. Cook for 1 minute to let the herbs bloom.
½ tsp dried oregano, ½ tsp dried basil, 1 tsp salt, ½ tsp freshly cracked pepper
Stir in the milk, and bring to a low boil. Stir constantly until it thickens slightly.
2 cups milk
Next stir in the vegetable broth. Add the potatoes.
4 cups vegetable broth, 2 lbs small red potatoes, quartered
Bring everything to a boil. Once boiling, reduce the heat to a gentle simmer. Partially cover the pot and cook for 10 - 15 minutes, or until the potatoes are tender.
Stir in the chopped frozen broccoli and cook for 2 more minutes, just until heated through.
2 cups frozen broccoli, chopped small
Taste and adjust the salt and pepper as needed. Ladle into bowls and enjoy!