Prepare your ingredients by washing and chopping the broccoli, dicing the onion, and mincing the garlic.

In a large pot over medium heat, sauté the diced onion in oil until translucent (about 5 minutes). Add the minced garlic and cook until fragrant.

Pour in the vegetable broth and bring to a simmer. Add the chopped broccoli and cook until tender (about 10 minutes).

Use an immersion blender to puree the soup until smooth or leave some chunks for texture.

Return to low heat, stir in milk or cream along with shredded cheddar cheese until melted. Season with salt and pepper.

Serve warm, garnished with extra cheese or croutons if desired.