Heat 2 tablespoons of olive oil in a large pot over medium heat. Add 1 medium chopped onion and sauté for about 5 minutes until translucent. Add 3 minced cloves of garlic and cook for an additional minute.

Stir in 2 peeled and diced medium potatoes and cook for around 5 minutes, stirring occasionally.

Pour in 4 cups of vegetable broth, increase heat to bring to a boil, then reduce to a simmer and cook for 10-15 minutes until potatoes are fork-tender.

Add 2 cups of broccoli florets and simmer for an additional 5-7 minutes until bright green and tender.

Blend the soup until smooth and creamy using an immersion blender or transfer in batches to a regular blender.

Return blended soup to the pot, stir in 1 cup of milk and 2 cups of shredded cheddar cheese over low heat until the cheese melts thoroughly.

Season with salt, pepper, and red pepper flakes, simmer gently for an additional 2-3 minutes.

Ladle into bowls and garnish with chopped parsley or chives if desired.