Begin by heating 2 tablespoons of olive oil in a large pot over medium heat. Add the chopped onion and sauté for about 5 minutes, until translucent and fragrant.

Introduce 3 minced garlic cloves to the pot and cook for an additional minute, stirring constantly.

Stir in 2 diced potatoes and allow them to cook for about 5 minutes, stirring occasionally.

Pour in 4 cups of vegetable broth and bring to a boil. Reduce heat to low and simmer uncovered for 10–15 minutes, until potatoes are fork-tender.

Add 2 cups of broccoli florets and continue to simmer for another 5–7 minutes, until bright green and tender.

Blend the soup until it reaches a smooth consistency using an immersion blender.

Return the blended soup to low heat and stir in 1 cup of milk or heavy cream and 2 cups of shredded sharp cheddar cheese.

Season with salt, pepper, and optional red pepper flakes. Heat through for an additional 2–3 minutes before serving.