Peel the carrots and chop them lengthways into strips, then sit them on top of each other and chop lengthways again so that they form long batons. Peel and chop the peppers in the same shape. Cut the garlic bulb in half across the middle (so that each clove is cut in half but leave the cloves connected). Slice the red onions in half lengthways and then finely across to give half rings.
Add the olive oil to the pan, then the vegetables, garlic, thyme and bay leaves. Sweat these for about 15 minutes until they have settled into the pan. Add the vinegar and honey and cook down for another 15 minutes or so until the veg are soft, but the carrots still have a little bite to them. Add a little water if necessary to create an oily coating around the vegetables. Season. Add parsley.
Season the mackerel on each side and grill under a hot grill (or you can bake them in a hot oven (180°C/350°F/gas mark 4). This should take no longer than 4 minutes in total. Mix the mackerel into the sweet and sour vegetables.
While you can eat this hot, it is best cooled and left in the fridge overnight. Take out a couple of hours before serving so it gets back to room temperature. If you want to be smart, you can lay the mackerel daintily on plates and spoon the pepper mixture over in an alluring fashion for a starter. Otherwise just serve it in a bowl in the middle of the table, with new potatoes and salad for a great summer lunch.