Preheat oven to 500°. Dry short ribs on paper towels and sprinkle with 1 tsp. each salt and pepper. In a large, heavy ovenproof pot, heat 1 tbsp. oil over medium-high heat. In 4 batches, brown ribs all over. Transfer to a bowl.
Cut squash wedges crosswise, put on a baking sheet, and toss with remaining oil. Roast until caramelized, 10 minutes. Remove from oven and lower heat to 300°.
Add onions and remaining 1 tsp. salt to pot and cook over medium-high heat, stirring often, until softened, about 3 minutes. Add flour and cook, stirring, until deep golden brown, about 5 minutes. Stir in garlic and cocoa; cook 1 minute. Stir in broth and brandy. Add dried cranberries, ginger, and orange zest and bring mixture to a boil. Return short ribs to pot, cover, and bake 2 1/2 hours.
Remove pot from oven and spoon off fat. (Or chill overnight before skimming; return to a simmer before continuing.) Stir in fresh cranberries and kabocha. Cover and bake until kabocha is tender and meat pulls away from the bone, about 30 minutes.
*Ask your butcher to cut the short ribs. To make squash easier to cut and peel, poke it all over with a fork, then microwave 2 to 3 minutes.
Note: Nutritional analysis is per serving.