Preheat the oven to 350°F. Grease a 9 x 5-inch loaf pan and line it with parchment paper, leaving some overhang for easy removal.
Whisk together the flour, baking powder, baking soda, and salt in a medium bowl.
In a large bowl, combine the granulated sugar and orange zest. Rub them together with your fingertips for about 30 seconds until the sugar smells strongly of orange.
Whisk the eggs, Greek yogurt, oil, orange juice, and vanilla into the orange-scented sugar until smooth.
Add the dry ingredients and gently fold with a rubber spatula just until no dry streaks remain. Do not overmix.
Pour the batter into the prepared loaf pan and smooth the top. Bake for 48–55 minutes, or until golden and a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let the cake cool in the pan for 10 minutes. Use the parchment overhang to lift it onto a wire rack and cool completely.
Whisk the powdered sugar, orange juice, and orange zest until smooth. Drizzle over the cooled cake and let the glaze sit for about 10 minutes before slicing.