Preheat the oven to 160°C fan and line a large baking tray with baking paper.
In a large bowl, beat the plant-based butter, olive oil, sugar, carob syrup, tahini, orange zest and vanilla well using a whisk or an electric mixer. Add the water and mix well.
In a separate bowl, combine the self-raising flour, wholemeal flour, baking powder, bicarbonate of soda, salt and cinnamon.
Gradually add the dry ingredients to the wet mixture and gently mix with a spatula or spoon, just until the ingredients are combined. The dough will be soft and oily. Do not overwork the dough, as it may start to release its oils.
Divide the dough into two equal portions and place them on the prepared baking tray. Shape each portion into a log approximately 20 cm long. If you prefer slightly longer-shaped rusks, gently press down on the logs with your hands to make them slightly flatter.
Brush the tops of the logs with the tahini and sprinkle generously with sesame seeds. Using a sharp knife, score each log into slices approximately 1 cm thick, without cutting all the way through.
Bake at 160°C fan for 30–40 minutes, until the logs are cooked through and lightly golden.
Remove the tray from the oven and leave the logs to rest for approximately 30 minutes, allowing them to cool enough to be sliced easily.
Cut the slices all the way through to separate the rusks. Turn each piece 90 degrees, so that the cut surface is facing upwards.
Reduce the oven temperature to 140°C fan. Return the rusks to the oven and bake for approximately 45 minutes, until they are thoroughly dried and crisp.
Leave the rusks to cool completely on a wire rack. Once completely cool, store them in an airtight container or biscuit tin.