Blood oranges have the most complex flavor of all the orange varieties.
Preheat oven to 350 degrees. Butter and flour a 5-by-9-inch loaf pan. With a vegetable peeler, remove peel from half of 1 orange, leaving pith. With a paring knife, cut rind into enough matchsticks to yield 1 tablespoon. Finely grate enough rind of remaining oranges to yield 1 packed tablespoon zest.
Working over a bowl, cut segments of 3 oranges free of membranes. Squeeze juice from membranes into a bowl (you should have 1/4 cup juice). Cut segments in half, and place in bowl with matchsticks of orange peel; set aside.
Combine sugar and zest in a bowl; using your fingers, rub together well. Add juice and buttermilk, and whisk to combine. Add eggs and oil, and whisk to combine. Sift together flour, baking powder, baking soda, and 1/4 teaspoon salt in a small bowl; add to buttermilk mixture, whisking until smooth.
Transfer batter to pan, and bake until golden and a toothpick inserted in the middle comes out clean, about 50 minutes. Let cool in pan on a wire rack for 15 minutes. Turn out cake onto rack, and let cool completely, about 2 hours. (Undecorated cake can be stored at room temperature for up to 2 days.)
Meanwhile, stir honey into bowl with orange segments.
Bring cream to a gentle simmer in a small saucepan. Pour over chocolate in a bowl, let stand for 5 minutes, and whisk until smooth. Drizzle ganache over cooled cake, and let set, about 1 hour. Serve with orange compote.