Melt the butter in a large pot or Dutch oven over medium heat. Add the onion, celery, and carrot. Cook until the vegetables soften, about 5 to 7 minutes.
Add the minced garlic and cook for 1 minute more until fragrant.
Whisk the flour into the vegetable mixture until fully incorporated, creating a roux. Cook for 1 minute, stirring constantly.
Slowly whisk in the broth, ensuring no lumps form. Bring the mixture to a simmer, stirring occasionally until it thickens slightly.
Stir in the milk and heavy cream. Reduce the heat to low and let the chowder warm through, but do not allow it to boil.
Add the corn kernels, Old Bay seasoning, thyme, and black pepper. Simmer gently for 5 minutes to allow the flavors to combine.
Remove the pot from the heat. Gently fold in the lump crab meat. Taste the chowder and add salt as needed.
Serve the rich crab chowder hot, garnished with fresh parsley.
Notes
For a lighter soup, substitute half-and-half for the heavy cream and use low-sodium broth.
If using frozen crab meat, thaw it completely and gently pat it dry before adding it to the soup.
To add a little heat, stir in 1/4 teaspoon of cayenne pepper with the dry seasonings.
This chowder pairs well with crusty bread or oyster crackers.