In a large soup pot set over medium heat, melt the butter and olive oil.
Next, add the diced onion, and sauté for about 3 minutes until they are soft and translucent. Add the minced garlic and sauté for 30 seconds.
Add flour to the pot and stir for 1 minute to cook off the floury taste. Next, add the stock a little at a time, whisking between pouring the stock. You want to ensure lumps do not form. After all of the stock has been incorporated, add in the whole milk or half-n-half. Stir until combined.
Bring the soup to a simmer and then add in the broccoli florets and roasted butternut squash. Next, add in the seasonings and allow the soup to simmer over medium heat for about 15 minutes, or until it has thickened.
Remove the soup pot from the heat and add the shredded white cheddar cheese. Stir until combined.
If it isn’t as thick as you would like, take 1 tablespoon of tapioca flour or cornstarch and add this into 1 tablespoon of cold water then add it to the soup. Cook for 1 minute until the soup thickens then serve.