Preheat oven to 375°. In a food processor, whirl flour, 2 tbsp. brown sugar, and 1/4 tsp. salt. Add cold butter and pulse until mixture resembles coarse crumbs. Add egg yolk and pulse to combine. Add 2 to 3 tbsp. ice water, pulsing until mixture begins to come together in a ball.
Press dough into bottom and up sides of a 9-in. round tart pan with 1-in. sides. Prick bottom of tart with a fork and chill in freezer 15 minutes. Bake crust until medium golden brown, 15 to 25 minutes, and remove from oven (leave oven on).
Meanwhile, in a standing electric mixer on high speed, beat whole egg, remaining 1/2 cup brown sugar, and remaining 1/4 tsp. salt until pale and ribbony, 7 to 10 minutes. Beat in melted butter, corn syrup, and rum.
Pour sugar mixture into tart shell and sprinkle with macadamia nuts. Bake tart until a knife inserted in center comes out clean, about 25 minutes. Cool tart on a wire rack at least 1 hour. Cut into wedges and serve with vanilla or ginger ice cream, if you like.
Note: Nutritional analysis is per serving.