In a pot, heat the olive oil over medium heat. Add the chopped onion and sauté until it turns translucent, about 3-4 minutes. Add minced garlic and sauté for an additional minute until fragrant.

Stir in the broccoli florets, coating them well with the onion and garlic mixture. Cook for about 2 minutes.

Add the chicken or vegetable broth and milk to the pot. Bring the mixture to a gentle boil, then reduce heat to a simmer. Allow to cook for about 10 minutes or until the broccoli is tender.

Using an immersion blender, carefully blend the soup until it reaches your desired smoothness. If you don’t have an immersion blender, you can transfer the mixture to a standard blender in batches.

Once blended, mix in the shredded cheddar cheese and Greek yogurt until fully incorporated. Season with salt and pepper to taste.

Allow the soup to simmer for another 3-4 minutes to let the flavors meld. Serve warm with your favorite toppings.