Remove lobster meat, keeping claws whole and cutting the tail into pieces, while reserving shells.
Mix flour and semolina, add eggs to a central well, and knead into a smooth dough for 5 minutes.
Wrap the dough ball in film and chill in the fridge for 30 minutes.
Sauté butter, shallot, fennel, lobster shells, and star anise in a pan until softened.
Add wine and reduce by half, then add stock and reduce by half, then add cream and reduce by one third.
Strain the sauce, stir in tomatoes and herbs, and season to taste.
Divide the rested dough into 4 pieces and roll out manually or with a pasta machine.
Dust with semolina and roll through settings until thin but sturdy.
Cut 9cm circles, place tail meat in the center, dampen edges, and fold into tortellini shapes.
Sauté courgette balls in butter and oil until colored.
Boil pasta in salted water for 3 to 5 minutes, then drain.
Serve 6 tortellini per bowl topped with sauce, claw meat, courgette, and cress.