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First, make the polenta crust. Bring the vegetable stock to a simmer in a medium saucepan and, working quickly, pour the polenta into the pan. Keep your pan over a low heat and, using a wooden spoon, stir constantly, beating any lumps that form. Continue stirring for 5-6 mins until the polenta is very thick.
Remove the pan from the heat, add the Gruyère and stir until the cheese has melted. Finally, stir through the beaten egg, season generously, and allow to cool slightly.
Lightly brush a baking sheet with oil. Tip the polenta into the centre and, using a spatula or oiled fingers, gently spread the polenta into a rectangle shape roughly the size of an A4 sheet of paper.
Heat oven to 200C/180C fan/gas 6. Smother a thin layer of pesto over the polenta, leaving a 1-1.5cm border around the edge of the tart. Top the pesto with slices of courgette, intermittently adding the sliced garlic and most of the basil. Season with ground black pepper and a good sprinkling of gruyère.
Cook on the middle shelf of the oven for 45 mins. Reduce the temperature to 180C/160C fan/gas 4 for a further 15 mins. Remove and allow to cool for 5-10 mins, scatter over the remaining basil and serve.