In a medium bowl, lightly beat the eggs with a fork. Add the mashed banana, yogurt, melted butter, and vanilla and stir to mix well. (The same fork works fine for this.) Pour the banana mixture into the dry ingredients, and stir gently with a rubber spatula, scraping down the sides as needed, until just combined. Do not overmix. The batter will be thick and somewhat lumpy, but there should be no unincorporated flour. Scrape the batter into the prepared pan, and smooth the top.