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.
Pour olive oil into a medium pot over medium-high heat. Add onion and cook, stirring often, until soft but not browned, about 4 minutes. Add rice and cook, stirring, until slightly translucent at edges, about 2 minutes. Add wine and cook, stirring often, until absorbed, about 3 minutes. Add broth, coconut milk, and salt. Stir just to combine, then cover, reduce heat to low, and simmer until rice is tender to the bite, 20 to 25 minutes.
Fluff with a fork and stir in orange peel.