Heat the oven to 180 C / 350 F. Grease a 23 cm / 9-inch round cake pan with 1 tsp butter and line the base with parchment. Pulse the 100 g pistachios in a food processor in 2-second bursts, about 15 to 20 seconds total, until they look like coarse sand. Stop there, because longer processing releases the oils and turns them into a paste that makes the cake dense.

Whisk the semolina, flour, ground pistachios, baking powder and salt in a medium bowl. In a large bowl, whisk the eggs and 150 g sugar for 2 minutes until pale and slightly thick. Whisk in the melted butter, yogurt, milk, lemon zest, vanilla and 1 tsp rose water. Fold in the dry mix until no streaks remain, then let the batter stand for 15 minutes so the semolina swells.

While the batter stands, simmer the 150 g sugar and 120 ml water in a 1.5-quart / 1.4 L saucepan over medium heat for 5 minutes, until it just coats the back of a spoon. Stir in the lemon juice and 1 1/2 tsp rose water, then set it aside to cool to room temperature.

Scrape the thick batter into the pan and smooth the top. Bake on the center rack for 32 to 35 minutes, until deep golden, the edges pull from the pan and a toothpick in the center comes out clean.

Right away, prick the hot cake all over with a skewer at 2 cm / 3/4-inch intervals. Spoon the cooled syrup over it in three additions, about a minute apart. It looks like a lot at first, but the crumb takes it in within 5 minutes. Leave the cake in the pan for 30 minutes.

Run a knife around the edge, invert the cake onto a plate, peel off the parchment and turn it right side up onto a serving plate. Scatter the chopped pistachios and rose petals over the top and cut into 10 wedges.