Trim Brussels sprouts and halve lengthwise. Cut shallot into very thin slices. In a 10-inch heavy skillet (preferably well-seasoned cast iron) melt 1 tablespoon butter with oil over moderate heat and cook garlic, stirring, until pale golden. Transfer shallot with a slotted spoon to a small bowl. Reduce heat to low and arrange sprouts in skillet, cut sides down, in one layer. Sprinkle sprouts with pine nuts and salt to taste. Cook sprouts, without turning, until crisp-tender and undersides are golden brown, about 15 minutes.
With tongs transfer sprouts to a plate, browned sides up. Add shallot and remaining 1/2 tablespoon butter to skillet and cook over moderate heat, stirring, until pine nuts are more evenly pale golden, about 1 minute. Spoon mixture over sprouts and sprinkle with freshly ground black pepper.
adapted from Gourmet, Sugar And Spice, February 1999, John Dombek, Santa Clara, UT