In a medium saucepan, combine the 8 oz sugar, lemon zest, lemon juice, and 6.8 fl oz water. Bring to a boil over medium-high heat, stirring occasionally to dissolve the sugar. Once boiling, reduce heat to medium and simmer for 2 minutes to create a light syrup base. Stir in the 3.5 oz rhubarb cut into 1-inch lengths and remove from heat. Let the syrup cool completely to room temperature—this will infuse the rhubarb flavor while you prepare the cake batter. I like to make this first so it has plenty of time to cool and the rhubarb becomes tender and flavorful.
Preheat your oven to 160°C (320°F) and lightly grease a 9-inch round cake tin or 8x8-inch square baking dish. While the oven heats, finely grind the 6 oz pistachios in a food processor until they resemble coarse flour with some small pieces remaining (you want texture, not a paste). In a medium bowl, whisk together the ground pistachios, 5.3 oz flour, 3.2 oz semolina, and 2 tsp baking powder. Set this dry mixture aside—having it ready lets you work smoothly when folding into the wet ingredients.
In a large bowl, beat the 5.5 oz softened butter and 5.5 oz sugar together until light, pale, and fluffy (about 3-4 minutes of beating). Add the 3 eggs one at a time, beating well after each addition to incorporate air and create a smooth emulsion—this helps the cake rise evenly and gives it a tender crumb. Stir in the 1 tsp vanilla extract. Gently fold in the dry ingredient mixture from Step 2, then fold in the 4.6 oz yogurt until just combined and no flour streaks remain. Fold in the 3.5 oz diced rhubarb pieces (the smaller pieces will distribute throughout the batter better than large chunks).
Pour the batter from Step 3 into your prepared tin, smoothing the top gently with a spatula. Bake in the preheated 160°C oven for about 1 hour, or until a skewer inserted into the center comes out with just a few moist crumbs (the cake should be golden on top and spring back slightly when lightly touched). The lower oven temperature helps the cake bake gently and evenly without over-browning the pistachio-semolina mixture.
Remove the cake from the oven and let it cool for 5-10 minutes until it's warm but no longer hot. Using a skewer or fork, poke holes all over the top of the cake in a regular pattern (about 1-2 inches apart). This creates channels for the cooled syrup to absorb into the cake layers. Slowly pour the cooled rhubarb syrup from Step 1 over the entire top surface, allowing it to soak in gradually. The warm cake will absorb the syrup beautifully, creating a moist, flavorful crumb.
Allow the cake to cool completely in its tin (about 1-2 hours, or until completely at room temperature). Once cooled, turn the cake out onto a serving plate or leave it in the tin if preferred. Top the cake with the soaked rhubarb pieces and extra syrup from Step 1, and scatter with extra crushed or whole pistachios for garnish and textural contrast. I find that letting the cake cool fully in the tin helps it stay moist and tender rather than drying out.
