Preheat the oven to 200°C and heat a griddle pan.
Brush mackerel with oil, season, griddle briefly on both sides, then bake for 2-3 minutes.
Sauté garlic and shallot in olive oil for 2-3 minutes in a large frying pan.
Add squash and star anise, cooking for one minute.
Pour in chicken stock and simmer for 4-5 minutes until the squash is tender.
Combine drained fennel, lettuce, and chicory in a large bowl.
Blend egg yolks, mustard, and lemon juice in a food processor.
Gradually add oil with the motor running until the dressing emulsifies.
Toss the salad leaves with the dressing.
Garnish squash with sesame seeds and parsley, plate it, and top with mackerel.