In a large frying pan, gently saute the garlic, shallots, chilli and diced fennel in the olive oil for 3 minutes. Add 2 tablespoons of the fennel seeds and also the thyme leaves. Cook the mixture down for a further 2 minutes.
Then, add the apple and the carrot. Continue to saute the mix for a further 3 minutes and then take off the heat. Place the mixture in the fridge to cool.
Once the mix has cooled, in a large mixing bowl, combine the pork mince with the vegetable mixture. Add salt, pepper and the breadcrumbs. Using your hands, combine the mixture until everything is just incorporated. You don't want to stir too much, or the mince will go tough once it has been cooked, due to overworking the protein.
Place the puff pastry sheets onto the bench and cut them in half, giving you 6 pastry sheets. Then, divide the mixture into 6 even portions. Form the mince into a long, thick sausage at one end of the pastry. Roll the pastry over the length of the sausage to create the sausage roll. Brush the sausage roll with egg wash and then slice into 3 identical smaller sausage rolls.
Transfer the sausage rolls, seam side down, to a baking tray lined with baking paper. Sprinkle with the black sesame seeds and leftover fennel seeds. Bake the sausage rolls for 25 minutes or until they are golden brown and cooked through.