Preheat oven to 350 degrees. Use coconut oil (or butter) to grease a 9-by-5-inch loaf pan. Grate zest from 2 oranges and place in a bowl with sugar. Rub ingredients together with fingers until sugar is evenly coated with zest.
Cut off bottom and top of orange and stand orange upright on a cutting board. Cut away peel. Cut up orange segments and place in bowl. Repeat with second orange. Break up segments to about 1/4-inch pieces.
Halve remaining orange and squeeze juice into a measuring cup. Add buttermilk or yogurt to juice until you have 2/3 cup liquid altogether. Pour mixture into bowl with sugar and whisk well. Whisk in eggs and olive oil.
In another bowl, whisk together flour, baking powder, baking soda and salt. With spatula, stir dry ingredients into wet ones. Fold in pieces of orange segments. Pour batter into prepared pan.
Bake cake for 50 to 55 minutes, or until it is golden and a knife inserted into center comes out clean. Cool on a rack for 5 minutes, then take out of pan and cool to room temperature right-side up. Serve with honey-blood orange compote (below) and whipped cream, if desired.
Honey-Blood Orange Compote: Cut up orange the same way as step 2. Drizzle in 1-2 teaspoons honey. Let sit for 5 minutes, then stir gently. When ready to serve, slice cake and spoon compote over cake, and serve with whipped cream.