Dice the onion, mince the garlic, and chop up the rest of the vegetables. Carrots and celery should be chopped into smaller chunks, while broccoli and cauliflower can be in medium to large chunks.

Prepare a pot to steam the broccoli, cauliflower, celery, and carrot. Fill the pot with 1-2 inches of water and bring to a boil. Then place vegetables in steamer for about 7 minutes until soft.

Melt butter in a pot at medium heat. Add onion and garlic, cook until tender (5-7 minutes).

Turn down heat slightly (to medium-low) and gradually whisk flour into the pot with the onion and garlic. Cook for about 3-4 minutes, until the mixture becomes slightly golden.

Gradually add half and half and chicken broth, stirring all the while. Add some salt and pepper to taste at this point. Bring to a simmer and cook uncovered until it thickens (about 20 minutes).

Add the steamed vegetables and cook (still at medium-low heat) for another 10-15 minutes.

If you want to purée the soup, let it COOL DOWN to near room temp, then put in a blender on purée mode. You may have to work in batches. If soup is still steaming a little, REMOVE the middle piece in the top of the blender cover so the steam can escape. Have a clean dish towel or paper towel to hover over the opening to minimize any mess. Combine puréed batches back into pot and warm it back up to then continue with step 8.

Add cheese to the soup (handful at a time) and stir until melted.