Begin by cleaning the langoustines: twist off the heads, then pinch and squeeze the shell edges to easily peel the tail meat. Remove the dark intestinal tract. Set the heads and claws aside for the bisque—do not discard them.
Using kitchen shears, cut off and discard the eyes from the heads to prevent bitterness. Detach the claws and crack them in half with a firm chop using the flat or heavy edge of a large knife.
Trim and finely chop the celery and carrot into small pieces.
Prepare the bisque: in a pan, heat a drizzle of olive oil over medium heat and add the two unpeeled, lightly crushed garlic cloves. Add the chopped celery and carrot, stirring to combine.
Let the vegetables sauté lightly, then add the langoustine heads and claws. Stir well and deglaze with the brandy. Allow the alcohol to evaporate, crushing the heads firmly with a ladle to extract their juices.
Cover the shells and aromatics with ice cubes (the thermal shock enhances flavor extraction) and let simmer for about 10 minutes.
Meanwhile, finely chop the raw langoustine tail meat with a knife to create a tartare. Transfer the tartare to a small bowl, season with a pinch of fine salt and a drizzle of extra virgin olive oil, and mix gently.
Once the bisque has simmered and reduced, strain it through a fine-mesh sieve into a bowl, pressing on the solids.
In a large skillet, heat a drizzle of olive oil with a few fresh marjoram leaves. Turn on the heat and pour in the lemon juice along with a ladleful of the prepared bisque.
Cook the egg tagliatelle in a large pot of boiling salted water for 2 minutes. Drain and transfer directly into the skillet with the lemon sauce; add a light drizzle of olive oil and toss vigorously to finish cooking and coat the pasta.
Plate the dish: twirl the tagliatelle using kitchen tongs and place onto serving plates. Shape the langoustine tartare into quenelles using two small spoons and arrange three quenelles on each plate. Finish with freshly grated lemon zest and serve immediately.
