To make the syrup, in a small saucepan, combine the sugar, orange zest strips and juice, cinnamon, cardamom, bay and ½ cup water. Bring to a simmer over medium-high, stirring to dissolve the sugar, then transfer to a 2-cup liquid measuring cup or small bowl; you should have about 1⅔ cups. Cool to room temperature.

Meanwhile, to make the cake, heat the oven to 350°F with a rack in the middle position. Mist a 9-by-2-inch round cake pan with cooking spray, line the bottom with a round of kitchen parchment, then mist the parchment.

Roll the thawed phyllo lengthwise, then slice the roll crosswise ½ inch thick.

Transfer to a rimmed baking sheet, using your hands to unfurl and separate the strips. Distribute in an even layer and bake until brittle and light golden brown, 15 to 18 minutes, scraping up and flipping the phyllo once about halfway through; it’s fine if many of the pieces break as they’re turning. Cool to room temperature on the baking sheet.

In a stand mixer with the paddle attachment, beat the sugar and grated orange zest on medium until fragrant, about 30 seconds.

With the mixer running on low, add the yogurt, oil, eggs, baking powder and salt. Increase to medium and beat until the mixture is well combined, about 1 minute, scraping the bowl as needed. Remove the bowl from the mixer and, if needed, scrape any zest that is stuck to the paddle attachment back into the bowl.

Add half of the phyllo to the batter base and, using a silicone spatula, fold until the phyllo is reduced in volume and almost evenly moistened. Add the remaining phyllo and fold until well combined and no dry patches of phyllo remain.

Pour the batter into the prepared pan and spread in an even layer without compressing the phyllo. Bake until deep golden brown and a toothpick inserted at the center of the cake comes out clean, 45 to 50 minutes.

When the cake is almost done, remove and discard the zest strips, cinnamon, cardamom and bay from the syrup.

Set the cake on a wire rack. Using a toothpick, immediately poke holes through the cake’s thickness every ½ inch or so. Slowly pour half the syrup evenly onto the warm cake, then let stand for about 5 minutes to allow the syrup to soak in. Slowly pour on the remaining syrup.

The cake will not immediately take in all of the syrup, so liquid will flood the pan; this is normal. Cool until room temperature and all the syrup has been absorbed, at least 2 hours.

Run a paring knife around the inside edge of the pan to loosen the cake, then invert onto a platter. Lift off the pan and peel off the parchment. Re-invert the cake onto a serving plate.