In a large skillet, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Add the shrimp to the skillet and cook for 2-3 minutes until they turn pink. Remove the shrimp from the skillet and set aside.
In the same skillet, add the cleaned mussels and chicken broth. Cover and cook for about 5 minutes until the mussels open. Discard any that do not open.
Reduce the heat to low, then stir in the heavy cream, lemon juice, red pepper flakes, salt, and pepper. Let it simmer for 2-3 minutes.
Return the cooked shrimp to the skillet and stir to combine. Cook for another 2 minutes until everything is heated through.
Serve immediately over cooked pasta or with crusty bread, garnished with fresh parsley.