Preheat oven to 350 degrees. Butter a 9-by-5-inch loaf pan. Grate zest from 2 oranges and place in a bowl with sugar. Using your fingers, rub ingredients together until orange zest is evenly distributed in sugar.

Supreme an orange: Cut off bottom and top so fruit is exposed and orange can stand upright on a cutting board. Cut away peel and pith, following curve of fruit with your knife. Cut orange segments out of their connective membranes and let them fall into a bowl. Repeat with another orange. Break up segments with your fingers to about 1/4-inch pieces.

Halve remaining orange and squeeze juice into a measuring cup; you’ll will have about 1/4 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. Gently 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 unmold and cool to room temperature right-side up. Serve with whipped cream and honey-blood orange compote (below), if desired.