Preheat the oven to 350 °F. Line a loaf pan with parchment paper with the edges hanging off to use for handles to lift out the baked bread.
In a large bowl, whisk together the eggs, oil, water, yogurt, maple syrup, and vanilla extract until smooth.
Mix in the almond flour, coconut flour, and baking powder until smooth.
Pour the batter into the prepared loaf pan and even the top with a spatula.
Bake in the oven for 50-60 minutes, until the top is golden, and a toothpick inserted in the center comes out clean.
Remove the bread from the pan by lifting it with the edges of the parchment paper onto a wire cooling rack. Allow the bread to cool completely and then slice. Freeze slices for later consumption or consume immediately.