Preheat the oven to 350°F (175°C). Grease your baking pan of choice. If you're using a loaf pan or round cake pan, line it with parchment paper.
Whisk the flour, salt, and baking powder in a medium bowl until combined.
Whisk together the yogurt, eggs, sugar, vanilla, and lemon zest in a large bowl until well blended.
Slowly whisk the dry ingredients into the wet ones. Stop when everything is fully combined and the batter is smooth.
Gradually mix in the oil, stopping as soon as everything is mixed together.
Pour the batter into the prepared pan, and bake at 350°F (175°C) on the center rack for 30-45 minutes. Check it with a toothpick starting at 30 minutes, and remove from the oven as soon as the toothpick comes out clean.
Allow the cake to cool for 10 minutes, and then remove it from the pan. Let it cool completely, then slice and enjoy!