In a medium-sized bowl, beat together eggs, sugar, and oil. Blend in the mashed banana and vanilla.
Whisk together and then sift the baking soda, baking powder, salt, cinnamon, nutmeg and flour. Add all at once to banana mixture. Mix quickly but thoroughly, then stir in the yogurt (I used sour cream) and nuts, mixing until just combined.
Pour the batter into a greased loaf pan. Bake the bread for about 1 hour, until a cake tester inserted in the center comes out clean. If the bread begins to brown too quickly, tent it with aluminum foil after 40 minutes in the oven.
When the bread tests done, remove it from the oven and place on rack for 15 minutes; after that, remove from pan and place on rack to finish cooling completely.