Preheat oven to 350 degrees. Butter a 9 x 4 inch loaf pan and set aside.
In a small bowl, mix the flour, baking powder and salt.
Whisk the eggs and sugar in a stand mixer on medium speed until light and fluffy, 3-4 minutes. Add the zest, vanilla and butter and mix, scraping down the sides once.
Add half of the flour, then half of the yogurt and mix. Add the remaining flour and mix, then the remaining yogurt.
Scrape into the pan and bake 40-50 minutes until it pulls away from the edges slightly, and feels firm to the touch. Let cool in pan 10 minutes then turn out onto a rack and cool completely.