Place the pine nuts in a dry frying pan set over a medium heat.
Toast until golden and aromatic before tipping into a food processor.
Add the basil leaves, parsley, cheese, and half of the olive oil. Pulse until broken down and coarse.
Blend on high, pouring in the remaining olive oil, until the pesto comes together.
Season to taste with salt, pepper, and some lemon juice. Transfer to a jar, seal well and chill until ready to use.
Place the drained sushi rice in a saucepan with 550 ml water.
Bring to the boil over a moderate heat, and then cover and simmer over a low heat for 15-20 minutes until the rice has absorbed the water.
Remove the pan from the heat and set aside to cool, still covered, for at least 10 minutes.
After 10 minutes, fluff with a fork and spread out on a large tray lined with clingfilm. Let cool until no longer warm to the touch.
Cover and chill until cold, about 2-3 hours.
Once cold, divide into 8-12 even portions, depending on size.
Shape half of them into puck shapes to form the bases of the burgers.
Shape the remaining rice portions into the tops of the buns, packing the rice into a small domed bowl or mould to form the tops.
Spread the bases with some of the prepared pesto before arranging some lettuce and basil leaves on top.
Top with the smoked salmon and then the shaped rice tops.
Press some sesame seeds into the tops of the burgers before serving.