Preheat oven to 350ºF. Generously spray a 9x5 inch loaf pan with nonstick spray.
In a separate mixing bowl, whisk together the flour, salt, baking soda and baking powder, set aside.
In a large bowl, beat together using a whisk, the Greek yogurt, sugar and olive oil together, then add the eggs one a time, whisking in each egg one at a time. Add vanilla if you want.
When the mixture is well blended, gently whisk in the dry ingredients.
Scrape it into the pan and smooth the top.
Bake the cake for 50 to 55 minutes, or until it is golden and starts to come away from the sides of the pan; a knife inserted into the center of the cake will come out clean or touching the top of the cake to make sure it's done. If your fingerprint leaves an indentation, it needs to bake more
Cool on a rack for 5 minutes, then run a knife between the cake and the sides of the pan.
Storing: You can keep the cake at room temperature for at least 4 days or freeze it for up to 2 months