Heat oil in a large saucepan over high heat. Add shrimp shells and cook, stirring frequently, until toasted, about 10 minutes.
Add onion, celery, carrot, leek, and garlic and cook for 3 minutes. Add 12 cups water, bay leaf, and thyme; bring to a boil. Reduce heat to medium and cook until reduced by half.
Strain stock, discarding solids; let cool to room temperature. Stock may be used immediately or transferred to an airtight container and kept refrigerated for up to 3 days or frozen for up to 3 months.