Prep all the vegetables: peel and dice the potatoes, dice the onion, mince the garlic, chop the broccoli into small florets, and shred the carrot.
Cook the bacon until crispy, then set aside to crumble later.
Shred the cheddar cheese.
Add a drizzle of olive oil to a large pot. Add the onion and garlic with a pinch of salt and cook over medium heat for 4 to 5 minutes.
Add the potatoes and broth, cover, bring to a boil, and let simmer for 15 minutes.
Using a blender (or immersion blender), blend the soup until smooth.
Add the broccoli and carrots and simmer for another 15 minutes, until tender.
Stir in the shredded cheddar until melted. Serve with crumbled bacon, a dollop of Greek yogurt, and green onion.