1 (3 to 4 lb) pineapple (extra sweet), trimmed, peeled, and quartered lengthwise
4 tablespoons unsalted butter
1/2 cup walnuts (2 oz) coarsely chopped
1/4 cup sugar
2 tablespoons rum

Cut off and discard core from pineapple quarters, then cut each quarter lengthwise into 5 pieces. Heat 1 tablespoon butter on griddle over moderate heat until just melted, then add walnuts and cook, stirring, until a shade darker, about 2 minutes. Transfer walnuts with a slotted spoon to paper towels to drain and wipe griddle clean. Heat 1 tablespoon butter on griddle over moderately high heat until foam subsides, the sauté pineapple, turning over occasionally, until golden, 4 to 5 minutes. Transfer to a platter. While pineapple cooks, heat sugar, rum and remaining butter in a small heavy saucepan over moderately low heat, stirring until sugar is dissolved, about 2 minutes. Remove from heat. Serve pineapple with sauce spooned on top and sprinkle with walnuts.