Whisk 1¼ cups (156 g) all-purpose flour, ½ teaspoon baking powderY ½ tsp. Diamond crystal or ¼ tsp. Morton’s Kosher Salt in a large bowl. Make a hole in the center and add 1 large egg, 2 tbsp. extra virgin olive oilY 2 tbsp. plain whole milk greek yogurt. Mix with a fork, then gradually incorporate the dry ingredients, mixing until just combined and a shaggy dough forms. Knead the dough in a bowl to bring together, then transfer to a surface and knead until cohesive and smooth, about 3 minutes. Wrap the dough in plastic and set aside at room temperature while you make the pilaf.
filling and assembly
Place a rack in the middle of the oven; preheat to 400°. Rinse 1 cup basmati rice in a fine mesh sieve under cold water until the water runs clear; drain and transfer to a small bowl. Drain 2 pounds frozen chopped spinach, thawed, in sieve, pressing to expel as much liquid as possible. Transfer to a kitchen towel and squeeze over the sink to expel any remaining liquid. Place spinach in a separate small bowl; Reserve kitchen towel.
Heat 2 tbsp. extra virgin olive oil Y 2 tbsp. chilled unsalted butter in a large Dutch oven or other heavy pot over medium-high heat. Cook 2 medium leeks, white and pale green parts only, thinly sliced, stirring occasionally, until softened and browned and crisp in spots, 5 to 7 minutes. Add rice and 2 tsp. Diamond Crystal or 1¼ tsp. Morton’s Kosher Salt and cook, stirring, until the kernels are translucent around the edges, about 1 minute. Pour in 1¼ cups plus 2 Tbsp. Water; stir to combine. Bring to a boil, then reduce the heat to low. Cover with a lid and cook 12 minutes.
Remove the pot from the heat, uncover, and spread the spinach over the rice. Cover pot with reserved kitchen towel, then lid; let stand 5 minutes. Fluff the rice gently with a fork and toss to distribute the spinach. stir in zest and juice of 1 lemon, 7 ounces feta, crumbled, ½ cup (packed) coarsely chopped dill, ⅓ cup golden raisins, ⅓ cup sliced almondsand remaining 2 tbsp. extra virgin olive oil. season with freshly ground pepper and more salt. Cool slightly.
Roll out the dough on a surface slightly floured surface to a 14″ round. (The dough will be very thin but quite elastic and pliable.) Brush the bottom and sides of a 9″ diameter pie plate with a little bit of melted unsalted butter. Decorate the bottom of the casserole as desired with dill sprigs, golden raisinsY laminated almonds. Transfer the dough to the skillet. Lift the edges and allow the dough to plummet into the pan, allowing the excess to hang over the sides; press dough into bottom and sides of pan.
Spoon into pan and spread into an even layer. Pulling the dough gently (a bit like stretching pizza dough), fold the edges up and over the filling, slightly overlapping in the center (it’s okay if the dough doesn’t completely cover the filling; no one will see the gap once that the cake becomes a sheet). Brush the dough with more melted unsalted butter to help seal.
Cover pan with foil and crimp lightly around edges. Bake the cake 20 minutes. Remove foil and continue baking until pastry is golden brown, 23–26 more minutes. Let cool 5 minutes, then invert cake onto a cake stand or large plate.
Combine 1 garlic clove, finely gratedY 1 cup plain whole milk Greek yogurt in a small bowl. Thin with water to a pourable consistency; season with salt.
Cut the cake into wedges with a serrated knife and serve with yogurt sauce for drizzling.