Prepare a narrow and tall mold, either round or rectangular (coat with a little oil and sprinkle with flour). A loaf pan works great.
Whisk the eggs, sugar, and salt in a large bowl for approximately 30 seconds until well mixed and airy.
Add the extra virgin olive oil and yogurt, and continue beating.
Incorporate the baking powder and flour a little at a time. Each time mix until it is all integrated.
Once all the ingredients are well beaten, pour the cake batter in the mold and bake for 40-45 min (do not open the oven for the first 30 min).
It is done when it is golden brown and a toothpick comes out clean.
Turn off the oven and let the cake rest inside with the door open for 15 min. Remove from the oven and let it rest for another 20-30 min before removing from the cake pan.