Preheat oven to 325°F with oven racks in top third and lower third of oven. Combine butter, granulated sugar, and muscovado sugar in bowl of a stand mixer fitted with the paddle attachment; beat on medium speed until light and creamy, 3 to 4 minutes. Add egg, and beat until combined. With mixer running on low speed, gradually add flour, vanilla extract, baking soda, and salt, beating until just combined, about 30 seconds. Stir in oats, chocolate, toffee, and apricots until just combined.

Line 2 rimmed baking sheets with parchment paper. Using a 1¾-inch scoop, drop mounds of dough (about 2 tablespoons each) onto prepared baking sheets, spacing dough mounds 1 ½ inches apart. Bake in preheated oven until cookies are lightly browned, 12 to 16 minutes, rotating pans top to bottom after 8 minutes. Let cookies cool on baking sheets 5 minutes. Transfer cookies to a wire rack, and let cool completely, about 30 minutes.