Preheat oven to 375°. Put flour and coconut milk in separate wide, shallow bowls. In another bowl, mix nuts and panko. Rinse chicken and pat dry. Sprinkle all over with salt and pepper.
Put 2 tbsp. butter and 2 tbsp. olive oil in a large frying pan over medium heat. Dredge chicken in flour, shaking off excess; dip into coconut milk, letting excess drip off; then press into nut mixture to coat on all sides. Reserve coconut milk. Lay chicken in frying pan in a single layer and cook until golden brown on the bottom, 3 to 4 minutes. With a spatula, turn pieces (taking care not to break off nut coating) and brown on the other side, 2 to 3 minutes longer. Transfer chicken to a baking pan and bake until no longer pink in center of thickest part (cut to test), 15 to 20 minutes.
Meanwhile, wipe any scorched nuts from pan with a paper towel. If pan is dry, add 1 tbsp. each butter and olive oil, then shallots, ginger, and garlic. Cook over medium heat, stirring often, until beginning to brown, about 5 minutes. Pour in broth, wine, and orange juice. Boil until liquid is reduced by about half, 8 to 10 minutes.
Pour mixture into a blender and, holding lid down tightly with a towel, whirl until very smooth. Return sauce to frying pan and add 1/4 cup reserved coconut milk (discard remainder) and salt and pepper to taste; stir over low heat until hot, then pour into a small bowl.
Spoon Coconut Pilaf onto plates, top with chicken, and serve with sauce.
*Chop the nuts by pulsing briefly in a food processor. Finely shred the peel from the oranges and save it for the pilaf.
Note: Nutritional analysis is per serving with 2 tbsp. sauce.