Cook the lobsters for 1 minute 30 seconds in salted simmering water, tying them beforehand to keep them straight. Glaze them and shell them.
Put the lobster eggs aside to dry, then mix them with the pumpkin seeds and the fleur de sel.
Break the heads of lobsters into 4 and fry them in the mixed oils. Once coloured, add the aromatic garnish and the tomato concentrate. 4 Deglaze the pan with white wine and Cognac and bring to a boil. Loosen with some water and cook for 50 minutes.
Pass through a sieve and strainer and reduce. Bind with cornstarch and season.
Make a classic kabocha purée: Mix the 300g of purée with the rest of the ingredients. Put in a whipping siphon and gas with 2 cartridges.
Bake the second kabocha squash cut in half on a bed of coarse salt for 45 minutes in an oven at 180°C. Chop the pulp with a knife and season with Banyuls vinegar.
Mix the pumpkin seeds with the egg white, salt and Espelette pepper. Spread on a silicone baking mat and bake at 160°C for 10 minutes.
Using a small spoon, make butternut balls. Cook for 5 minutes in the pickle mixture and let cool.
Remove the flesh from the lobster claws and sweat it with the finely diced squash, moistened with the lobster mixture, then season with the remaining ingredients.
Hollow out the mini pumpkins and fill them with the lobster stew. Finish with the pickle balls. Reheat the lobsters in clarified butter and serve.