Preheat your oven to 400°F (200°C). Toss the garlic cloves with a little olive oil and wrap them in foil, then roast in the oven for about 20 minutes until soft and caramelized.
While the garlic roasts, chop the cauliflower, potato, and onion into similar-sized pieces.
In a medium pot, warm the remaining olive oil over medium heat. Sauté the chopped onion until translucent, about 3-4 minutes.
Add the cauliflower and potato to the pot, and pour in the vegetable broth. Bring the mixture to a simmer and cook until the vegetables are tender, approximately 15 minutes.
Meanwhile, cook the chicken breast by either grilling or poaching until fully cooked through. Once cooled, shred or dice into small pieces.
Squeeze the roasted garlic out of its skins and add it to the pot along with the rinsed cannellini beans. Let it all simmer for another 5 minutes.
Remove the pot from heat and use an immersion blender to blend the soup until smooth, leaving a bit of texture if desired.
Stir in the Greek yogurt to add creaminess, then fold in the cooked chicken breast pieces.
Season with salt and pepper to taste, and serve warm.