Cut vegetables into equal-size chunks, cover with water, and bring to a boil. When the vegetables are semi-soft, add a handful of chopped parsley and the peeled cloves of garlic.
Once all of the vegetables are soft enough to easily cut with a butter knife, drain the water, add cream and return to stovetop. Use a potato masher to mash the vegetables until smooth, then add in the cheese a cup at a time, slowly stirring it in. If desired, stream in a bit more cream to achieve a smoother consistency.
Serve with additional grated cheese and parsley.