1. Heat a large pot over medium heat. Add shrimp shells and cook, stirring occasionally, until they turn pink and start to brown, about 5 minutes.
2. Add onion, celery, carrot, and garlic. Cook, stirring occasionally, until vegetables begin to soften, about 5 minutes.
3. Stir in tomato paste and cook for another minute.
4. Add water, salt, peppercorns, thyme, and bay leaf. Bring to a boil, then reduce heat and simmer uncovered for 30 minutes.
5. Strain the stock through a fine-mesh strainer, discarding solids. Let cool before storing.