In a large pot, heat olive oil over medium heat. Add chopped onions and minced garlic. Sauté until onions are translucent.
Add frozen broccoli florets and diced potato to the pot. Stir to combine with onions and garlic.
Pour in the vegetable or chicken broth. Bring the mixture to a boil, then reduce heat to simmer. Cover and cook until the vegetables are tender, about 15-20 minutes.
Using an immersion blender or transferring in batches to a regular blender, puree the soup until smooth.
Stir in the milk or cream. Adjust the consistency by adding more liquid if needed. Season with salt and pepper to taste.
Ladle the soup into bowls. Garnish with shredded cheddar cheese and serve with croutons or crusty bread.
