Bring milk, half & half, and heavy whipping cream to a boil.
When it starts to boil, make a paste (or slurry) in a separate bowl with the cornstarch and cold water. Be sure to whisk well until the paste is fully blended.
Add the paste to the soup and bring back to a boil for 1 minute, mixing constantly.
If the soup seems too thin, make more paste with 1 T. corn starch & 1 T. cold water. Mix into the soup and heat through again, mixing constantly.
Keep adding the 1 tablespoon cornstarch/1 tablespoon cold water paste until your soup gets to the preferred thickness.
Then add your crab meat.
Adding crab meat after the cornstarch paste is so that you don't break up the delicate chunks of crab while whisking the cornstarch.
Add fresh parsley, Old Bay Seasoning, butter, salt and pepper and heat through.
Add extra crab meat & Old Bay Seasoning based on your preferences.
Remove from heat.
Soup is ready to serve.