Combine warm water, sugar, and yeast. Let sit 5 to 10 minutes until foamy.
In a stand mixer bowl, whisk together bread flour, whole wheat flour, cocoa powder, and salt.
Add yeast mixture, softened butter, honey, molasses, and oil to the dry ingredients. Mix on low for 2 minutes then medium for 8 to 10 minutes until smooth and elastic.
Place dough in a lightly oiled bowl, cover, and let rise for 1 to 1½ hours until doubled.
Punch down dough. Divide into two equal pieces. Shape each into a smooth oval loaf about 6 inches long.
Brush each loaf with softened butter or water, then roll firmly in oats until fully coated. Press oats in gently all over.
Place on a parchment-lined baking sheet. Cover and let rise for 45 minutes to 1 hour until puffed.
Preheat oven to 375°F (190°C). Score each loaf with 2 to 3 diagonal slashes. Bake for 22 to 25 minutes until firm and hollow-sounding when tapped.
Cool on a wire rack for at least 15 minutes before slicing. Serve warm with soft butter.