Preheat the oven to 200°C (180°C fan) or Gas Mark 6.
Rinse the shrimp shells briefly to remove any grit, then pat dry.
Spread the shrimp shells in a single layer on a roasting tin.
Drizzle the olive oil and sprinkle the salt over the shells, then toss or shake the tin to coat evenly.
Roast the shells for 10–15 minutes until crisp and lightly browned.
Place the roasting tin on a medium hob burner (or transfer the roasted shells to a saucepan if your tin is not hob-safe).
Carefully pour the 2.5 litres of boiling water over the roasted shells and bring to a gentle simmer.
Simmer for 10–15 minutes, tasting and adjusting strength by simmering longer or adding a little water if too strong.
Strain the stock through a fine-mesh colander into containers, discarding the shells, then cool and store in the fridge or freezer as needed.