In a saucepan, add a tablespoon of oil and lightly brown the shells and heads for 3-4 minutes over medium-high heat. Press on the shrimp heads to extract the flavorful juices.
Add water, bay leaf, 1 teaspoon kosher salt (use less for table salt), and some black pepper.
Let it boil, then lower the heat to simmer for 5 minutes.
Strain the stock through a fine-mesh strainer, then discard the solids.