Heat the oven to 375 °F and use the tahini to brush the bottom and sides of a 9x13-inch baking dish. Spread the coating evenly so no thick streaks collect along the edges.
Combine the yogurt, sugar, baking powder, and baking soda in a bowl, then leave it aside while preparing the semolina. A little bubbling and expansion show the expected reaction in the yogurt mixture.
Work the melted butter through the semolina in a separate bowl, then fold in the fine coconut flakes. The grains should look evenly moistened and begin to cling together.
Incorporate the yogurt mixture into the coated semolina, then stir in the milk until evenly combined. Stop once the batter is cohesive, thick, and spreadable, without dry pockets.
Transfer the batter to the tahini-coated dish, level the surface, and tap the dish against the counter to release trapped air. An even layer helps the cake bake consistently across the pan.
Use a knife to mark squares or diamonds in the unbaked batter, making approximately 24 portions. The mixture should be firm enough to retain the cutting lines.
Gently press a whole almond into the middle of each marked portion and, if desired, scatter a little fine coconut over the surface. Keep the almonds visible rather than burying them in the batter.
Bake uncovered on the bottom rack for 25–30 minutes, then transfer the dish to the top rack for another 5–10 minutes. Look for browning edges before moving the dish and an evenly light brown top before removing it.
During baking, heat the syrup sugar and water together, stirring until dissolved, then simmer for about 8 minutes and finish with a squeeze of lemon. The syrup should thicken slightly while remaining fluid enough to pour.
Immediately after baking, follow the marked lines with a sharp knife and distribute the warm syrup over the entire hot cake. The reopened cuts help the syrup reach into the crumb rather than staying only on top.
Leave the cake in its dish until completely cool, allowing at least 1 hour before lifting out portions. The syrup needs time to absorb and the delicate crumb needs time to settle so the pieces hold together.