Peel the carrots and onion, then finely chop them with the celery stalks.

Separate the langoustine heads and shells from the tails, then peel the tails and reserve them chilled.

Heat 2 tablespoons of extra virgin olive oil in the large skillet, then sauté the chopped vegetables for 8 minutes over medium heat.

Add the langoustine heads and shells to the skillet, then cook while pressing them with the wooden spoon for 5 minutes.

Add 1 litre of water to the skillet, then simmer the shell stock for 20 minutes.

Strain the langoustine stock through the fine-mesh strainer, then discard the shells and vegetable solids.

Blend the strained stock until smooth, then keep the langoustine cream warm over very low heat.

Halve the cherry tomatoes, then chop the parsley leaves.

Bring the remaining 3 litres of water to a boil in the large pot, then salt the water lightly.

Cook the paccheri in the boiling water until very al dente, then reserve 250 ml of pasta cooking water.

Melt the salted butter with the remaining 1 tablespoon of olive oil in the large skillet, then sauté the langoustine tails for 2 minutes.

Add the halved cherry tomatoes to the skillet, then cook for 3 minutes until lightly softened.

Add the drained paccheri and langoustine cream to the skillet, then toss for 2 minutes while adding pasta water as needed.

Season the pasta with black pepper, lime zest, and lime juice, then fold in the chopped parsley.

Taste and adjust the salt, then serve the paccheri immediately with the langoustine tails and cherry tomatoes.