Preheat oven to 375°. In a large bowl, cream salted butter with 1/2 cup sugar until light and fluffy. Add egg and egg yolk and beat to combine. Gradually add flour and mix well (dough will be very soft). Transfer to a floured 16- by 11-in. parchment paper. With a floured rolling pin, roll dough to same size as parchment. Trim any overhang, then transfer dough (on parchment) to a large rimmed baking pan. Bake until golden brown, about 12 minutes. Remove from oven (leave oven on) and set aside.
In a medium saucepan over medium heat, stir together unsalted butter, remaining 1 1/4 cups sugar, honey, and cream. Cook mixture, stirring frequently, until it registers 250° on a candy thermometer. Remove pan from heat and stir in almonds, raisins, apricots, and cherries.
Using a spatula, gently spread warm topping over shortbread. Bake until topping is caramelized and almonds are lightly browned, about 10 minutes. Remove from oven; while still warm, cut into 2-in. squares. Cool completely.
Note: Nutritional analysis is per bar.