To make the pesto, blitz all the ingredients apart from the salt and pepper in a food processor or mixer. Season with salt and pepper. Set aside the pesto.
Preheat the oven to 180 °C fan. Slice the sweet potatoes and potatoes. Roughly wash the carrots but do not peel, cut into long, wide strips. Using a steamer basket, cook the vegetables over boiling water for 10 mins., rinse in cold water. Line a greased cake tin with the spelt pastry. Prick the base evenly with a fork. Brush the edges with pesto and roll inwards. Bake the pastry base in a preheated oven for 10 mins., allow to cool. Using a handheld blender, puree the silken tofu, turmeric and salt. Cover the pastry base with the remainder of the pesto and the steamed vegetables. Top with the silken tofu mixture and bake for 15 mins. Remove the tart from the oven, sprinkle with sesame seeds and pepper, bake for a further 5 mins.