Prepare the Base In a large pot over medium heat, melt the butter. Add the diced onion, carrots, and celery, cooking until the onion is translucent and vegetables have softened, about 5 minutes.
Make the Roux Sprinkle the flour over the cooked vegetables, stirring constantly for 1-2 minutes to eliminate the raw flour taste. This will help thicken the chowder.
Add Potatoes and Broth Gradually add the vegetable broth while stirring to avoid lumps. Add the diced potatoes, thyme, Old Bay seasoning, and bay leaves. Sprinkle in a dash of salt and pepper. Cover the pot and let it simmer for approximately 15 minutes, or until the potatoes are perfectly tender.
Add Milk and Shrimp Pour in the milk and stir well. Add the shrimp, and cook for another 5-7 minutes, or until the shrimp are opaque and cooked through.
Serve Remove the bay leaves before serving. Ladle the chowder into bowls, and garnish with a sprinkle of fresh herbs or a dash of Old Bay for added flavor.