Heat the oven to 180°C and line a 25 x 25cm deep baking tin with baking paper.
In a large bowl, beat together the sugar and lemon zest, until the sugar is the consistency of damp sand. Add the eggs and oil to the mixture and beat until smooth and well combined. Add the polenta, ground almonds, baking powder and salt and fold in until well combined, then fold in the zucchini.
Scrape the batter into the lined tin and bake for 25–30 minutes, until just beginning to turn pale golden.
Meanwhile, make the syrup. In a small saucepan, heat the lemon juice and caster sugar, stirring until the sugar has completely dissolved and a warm syrup has formed.
Evenly sprinkle the chopped pistachios and dried rose petals over the surface of the still-warm cake, then use a spoon to drizzle over the warm lemon syrup.
Let the cake cool completely, then turn out of the tin and cut into slices or squares.