Melt butter in the slow cooker on high setting or in a skillet. Add diced shallot and cook for 2 to 3 minutes until softened. Add minced garlic and stir constantly for 30 seconds. Stir in tomato paste and cook for another minute to caramelize slightly.

Pour fire-roasted tomatoes with their juice and seafood broth into the slow cooker. Add Old Bay seasoning, smoked paprika, Italian seasoning, salt, and white pepper. Stir well and simmer on low for 15 to 20 minutes to let seasonings infuse.

Cut softened cream cheese into chunks and add to the slow cooker. Stir constantly for 2 to 3 minutes until completely dissolved and blended into the broth for a velvety texture.

Pour in heavy cream and whisk in freshly grated Parmesan cheese until fully combined. The mixture should look creamy and slightly thick.

Add the peeled and deveined shrimp to the slow cooker and stir gently. Cook on low for 3 to 5 minutes until shrimp turn pink and opaque. Watch carefully to avoid overcooking.

Taste the bisque and adjust salt and white pepper as needed. Ladle into bowls and top with fresh snipped chives. Serve immediately with crusty sourdough rolls on the side.