Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper. Chop cauliflower into florets and toss them in 1-2 tablespoons of olive oil, salt, and pepper. Place on the baking sheet alongside a whole head of garlic wrapped in foil.

Roast the cauliflower and garlic in the preheated oven for 30-35 minutes, flipping the cauliflower halfway through. It should be tender and golden.

In a large pot, warm the remaining olive oil over medium heat. Dice the onion and sauté for 5-8 minutes until translucent.

Squeeze the roasted garlic from its skins into the pot. Add the roasted cauliflower and vegetable broth. Blend until smooth using an immersion blender or countertop blender.

Return the blended mixture to the pot over medium heat. Stir in the shredded sharp cheddar cheese until melted and velvety.

Taste and adjust seasoning with salt and pepper. Garnish with chopped green onions or extra cheddar before serving.