Add the plain yogurt and granulated sugar to a large mixing bowl and whisk together.
Add the vegetable oil and mix well.
Add the eggs and whisk until combined.
Grate fresh orange zest into the mixture.
Whisk the wet ingredients until smooth and evenly combined.
In a separate bowl, combine the all-purpose flour, baking soda, baking powder, and salt.
Mix the dry ingredients into the wet mixture.
Add the cocoa powder and whisk until the batter is evenly chocolate-colored.
Add the orange extract, orange juice, and water, then mix until a smooth cake batter forms.
Pour the batter into a prepared loaf pan.
Bake at 350°F (175°C) for 45–55 minutes, or until cooked through.
Let the cake cool completely before removing it from the pan, slicing, and serving.
