Preheat your oven to 400 degrees F. Line a baking sheet with parchment paper to prevent sticking.
Add the cauliflower florets to the pan and drizzle with 1 to 2 tablespoons of olive oil. Season generously with salt and pepper; toss to combine.
Prepare the garlic: Peel off the outer papery layers of the whole head, leaving the skins intact on the individual cloves. Cut a ¼ inch off the top of the cloves to expose them.
Wrap the garlic in a piece of foil and drizzle the top with a little olive oil. Loosely wrap the foil around the garlic, and place it on the baking sheet with the cauliflower.
Roast the cauliflower and garlic for 30 to 35 minutes, flipping halfway through, until the cauliflower is golden and caramelized.
While they roast, heat 1 tablespoon of olive oil in a pot over medium heat. Add the diced onion and sauté for about 5 to 8 minutes until the onion is translucent.
Once the cauliflower and garlic are done roasting, squeeze the roasted garlic out of its skin into a large blender along with the sautéed onion, roasted cauliflower, broth, salt, and pepper. Blend until smooth for about 1 minute.
Transfer the blended mixture back to the pot and place it over medium heat. Allow it to come to a light simmer. Stir in the cheddar cheese and let it melt, stirring occasionally for about 10 to 15 minutes.
Taste and adjust the seasonings as necessary. Serve hot, garnished with sliced green onion and extra cheddar cheese on top.
