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Preheat the oven to 350ºF. Rub a little butter on the inside of a loaf pan to coat the bottom and sides.
Mash the banana well, then add it to a large bowl along with the yogurt, eggs, sugar, melted butter, and vanilla. Whisk these ingredients until they're well combined.
In a separate bowl, stir together the flour, baking powder, baking soda, salt, and nutmeg until well combined.
Pour the dry ingredients into the bowl of wet ingredients and stir together just until there is no dry flour left on the bottom of the bowl (a few lumps are okay, just be careful not to over stir). Gently fold in the chopped walnuts.
Pour the batter into the prepared loaf pan, then bake in the preheated 350ºF oven for 60 minutes, or until the bread is brown, cracked open on top, and a toothpick inserted in the center comes out clean (a few moist crumbs are okay, just no raw batter).
After baking, let the banana bread cool in the pan for about 15 minutes. Once it's slightly cooled it will have pulled away from the bread pan slightly. Run a knife along the sides between the bread and pan, then gently turn the loaf out onto a wire rack to finish cooling. Once cool, slice and serve.