First, make the cake. Position a rack in the center of the oven and preheat the oven to 350°F. Spray a 9 x 5-inch loaf pan with cooking spray and line it with parchment paper, leaving a 2-inch overhang on the long sides. Spray the parchment, too. Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt.
Prep the sugar. In a small bowl, combine the sugar and blood orange zest. Use your fingers to rub the zest into the sugar—this will infuse the sugar with oils from the zest.
Mix the wet ingredients, then add the sugar. In a large bowl, whisk the eggs until the yolks are broken. Add the yogurt, oil, blood orange juice, and orange extract until combined. Add the sugar and zest and continue whisking until smooth.
Add the dry ingredients. Gradually whisk in the dry ingredients until just combined. The batter will be lumpy, but it’s totally okay, I promise!
Bake the cake. 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. Next, make the blood orange soak. While the cake cools, make the blood orange soak. Combine the sugar and blood orange juice for the soak in a small, heavy-bottomed sauce pan. Bring to a boil over medium heat, whisking to dissolve the sugar. Once boiling, remove from heat and immediately whisk in the orange extract. Soak the cake. Use a pastry brush to brush the warm syrup over the top of the still warm cake. 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. Cool completely on a wire rack. Make the glaze. Once the cake is cool, make the glaze. In a medium bowl, whisk together the confectioners’ sugar, blood orange juice, and salt for the glaze until smooth. Pour the glaze over the top of the cake and use an offset spatula to spread it into a thin layer on top of the cake. Let any excess glaze drip off and transfer to a wire rack to dry for 1 to 2 hours. Serve and store. The blood orange drizzle cake can be stored at room temperature, wrapped tightly in plastic wrap, for up to 3 days.