Preheat the oven to 350°F (180°C) and spray a 9-cup Bundt pan with baking spray.
In a medium bowl, whisk together the flour, baking powder, and salt.
In a large bowl, beat the eggs using a handheld or stand mixer until frothy, about 1 minute.
Add the sugar and continue beating for 2 minutes until the mixture is pale and slightly thickened.
Add the oil, yogurt, and vanilla extract, and mix until fully combined.
Add the dry ingredients to the wet mixture. Mix on low speed until just combined. Do not overmix.
Pour the batter into the prepared Bundt pan and smooth the top with a spatula.
Bake for 45 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then turn it out onto a wire rack and cool completely before slicing.