Preheat oven to 350 degrees. Line two baking sheets with parchment paper; set aside. In a large bowl, sift together flour and baking soda.
In the bowl of an electric mixer fitted with the paddle attachment, cream the butter and both sugars on medium speed until light and fluffy, 2 to 3 minutes, scraping down the sides of the bowl once or twice during mixing. Add the egg; mix on high speed to combine. Add the vanilla; mix to combine. Scrape down the sides of the bowl.
Add flour mixture to egg mixture, and mix on low speed until well combined. Add the oats, cherries, chocolate, and toffee pieces; mix to combine after each addition.
Spoon a heaping tablespoon of dough onto a lined baking sheet. Repeat, spacing 2 inches apart.
Bake cookies until golden brown, 14 to 16 minutes, rotating baking sheet halfway through. Transfer to a wire rack to cool. Store in an airtight container up to 2 days.