Preheat the oven to 375 degrees F. Line 2 baking sheets with parchment paper. Whisk the flour, baking soda and salt in a medium bowl. Beat the butter, espresso powder and brown sugar in a large bowl with a mixer on medium-high speed until light and fluffy, about 3 minutes. Beat in the egg and vanilla until smooth. Reduce the mixer speed to low, then gradually beat in the flour mixture until just combined. Stir in the dark chocolate chips and toffee bars.
Roll the dough into 1 1/2-inch balls and arrange 2 inches apart on the prepared pans. Bake, switching the pans halfway through, until the cookies are puffed and just set around the edges, about 15 minutes. Let cool 10 minutes on the pans, then transfer to a rack to cool completely.
Melt the white chocolate chips in the microwave in 30-second intervals, stirring, until smooth. Drizzle over one side of each cookie and decorate with sprinkles. Refrigerate until set, about 30 minutes.