Bring a large pot of water to a boil. Add the cauliflower and cook for 7-9 minutes, until fork-tender. Drain and set aside.

Heat a large pot over medium heat. Add the butter and oil. Once melted, add the garlic and cook for 1 minute, until fragrant. Stir in the cornstarch along with a pinch of salt and pepper, stirring until a paste forms.

Add the vegetable broth and whisk to combine. Bring the mixture to a boil, then stir in the chopped broccoli. Cover and cook for 12-15 minutes, until the broccoli is tender.

Meanwhile, add the cooked cauliflower and cottage cheese to a blender. Blend until smooth. If needed, add a small drizzle of water to help it blend.

Once the broccoli is cooked, turn off the heat, remove the lid, and let cool for about 5-10 minutes. If the temperature is too high, it will affect the texture of the cottage cheese, so do not skip the cooling step. Stir in the shredded cheese and cauliflower mixture. Return the pot to low heat and cook just until the cheese melts and the soup is warmed through. Serve.