Heat the olive oil in a large pot over medium heat. Add the diced onion and cook for 4 minutes until it softens.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the frozen broccoli florets and vegetable broth. Bring the mixture to a simmer and cook for 10 minutes until the broccoli is tender.
Remove the pot from the heat. Use an immersion blender to puree the soup until smooth, or transfer it in batches to a countertop blender.
Return the pot to low heat. Stir in the low-fat milk, salt, and black pepper.
Gradually add the shredded cheddar cheese, stirring until it melts completely and the soup thickens slightly. Serve right away.