Preheat the oven to 350 (F), and butter your loaf pan liberally. Dust with flour and tap out any excess.
Whisk 1 1/2 cups flour, 2 teaspoons baking powder, and 3/4 teaspoon kosher salt in a medium bowl. Set aside.
Using your fingers, rub together 1 cup sugar and 1 tablespoon lemon zest in a large bowl until sugar is moist. Whisk in 3/4 cup Greek yogurt, 1/2 cup vegetable oil, 2 eggs, and 1/2 teaspoon of vanilla extract until well combined.
Using a rubber spatula, fold in the flour/baking powder/salt mixture (from the second step) into the sugar/yogurt/oil mixture (from the third step), just until smooth and combined.
Pour batter into the prepared pan and smooth top. Bake for 50 - 55 minutes, or until the top of the cake is golden brown and a skewer inserted into the center comes out clean.
Let cake cool in pan on a cooling rack for 15 minutes. Invert onto rack and cool completely.