Mix all the marinade ingredients in a wide, shallow bowl, adding a little salt. Add the chicken breasts and turn them to coat thoroughly. Cover with cling film and leave for 1 hour, turning them halfway.
Cut the fennel lengthways into 5mm/¼in thick slices. Blanch in salted boiling water for 5 minutes, refresh and drain.
Cut the carrots into 5mm/¼in diagonal slices. Do not cook the vegetables together. Score the surface, then blanch for 3 minutes, refresh and drain. Lightly brush the fennel and carrots with olive oil.
Heat a griddle pan until smoking hot. Add the fennel first, then the carrots and griddle for 5-10 minutes, giving them a quarter-turn to mark attractively. Turn them over and repeat on the other side. Season, place on a plate and keep hot.
Put the chicken breasts in the hot griddle pan, skin side down. Once they are marked with lines, quarter-turn to make a lattice pattern. Turn them over, lower the heat and give them a quarter-turn as before. Cook for 12-15 minutes in total, depending on thickness.
Arrange the fennel slices on plates and top with the chicken. Place the carrots alongside. Put a knob of butter on each chicken breast and top with fennel seeds.