Roughly chop vegetables and garlic. Heat oil and butter in a large and heavy bottomed pot. Sweat onions and garlic in oil and butter over a low-medium heat, with a small amount of salt (very little is needed, because the cheese will add salt later). This should take about 5-10 minutes.
Then add the potato, cauliflower and carrots. Season with a little more salt and pepper. Stir until the vegetables are all glazed with the butter and oil. Cover and cook over a low heat for about 15-20 minutes.
Cover the ingredients with the broth and milk. Add thyme and bay leaf. Cover and bring to a boil. Once boiling, lower heat to a simmer and add lemon juice and wine. Simmer for about 30-45 minutes.
While the soup is simmering, grate your cheese. If you are like me, you may need to buy some extra cheese so you can munch while you grate. Check to make sure the vegetables are all soft (a fork should easily be able to pierce them). Once your vegetables are softened, blend your soup. I use an immersion blender, but any should do. f you like a thicker consistency, cook the soup down. Or, if you prefer your soup a little thinner, add more broth or milk. Once it is to your liking, slowly add your cheese, a handful at a time. Whisk as you go.
I like to garnish with freshly chopped chives, but have fun and be creative enjoying this rich and yummy soup.