Center a rack in the oven and preheat the oven to 350 (F). If using a citrus loaf cake pan (see baker’s notes), generously spray the pan with cooking spray. If using a traditional 9 x 5-inch loaf pan, spray with cooking spray and line it with parchment paper, leaving a 2-inch overhang on the long sides. Spray the parchment, too.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a small bowl, combine the sugar and lemon zest. Use your fingers to rub the zest into the sugar—this will infuse the sugar with oils from the zest.
In a large bowl, whisk the eggs until the yolks are broken. Add the Stonyfield Organic Whole Milk Greek Plain Yogurt, oil, lemon juice, and extract until combined. Add the sugar and zest and continue whisking until the sugar is completely moistened.
Gradually add the dry ingredients to the wet ingredients and whisk until there are no lumps and the batter is smooth.
Pour the batter into the prepared pan and use an offset spatula to smooth the top. Set the loaf pan on a sheet pan and bake for 60 to 65 minutes, or until a skewer inserted into the center of the loaf cake comes out with a few crumbs attached. Cool on a wire rack.
While the loaf cake is cooling, make the simple syrup. Combine the sugar and lemon juice in a small, heavy-bottomed sauce pan and bring to a boil over medium heat, whisking to dissolve the sugar. Once boiling, remove from heat and immediately whisk in the lemon extract.
Use a pastry brush to brush the drizzle over the loaf cake while both the cake and syrup are still warm. If using a citrus loaf pan, you’ll need to turn out the loaf onto a serving platter before brushing with the drizzle (see baker’s notes). If using a traditional 9 x 5-inch loaf pan, there’s no need to turn out the loaf. Use the syrup completely—it will seem like there’s too much for the loaf. You’ll need to wait for a layer of drizzle to absorb before brushing the cake with the syrup again. Serve warm, or at room temperature. The lemon drizzle cake can be stored at room temperature, wrapped tightly in plastic wrap, for up to 3 days.