Put the peppermint candies into a plastic bag and crush them coarsely with the flat side of a meat mallet. Using a large sieve, sift candy pieces, discarding fine powder; set candy pieces aside.
Line the bottom of an 8"x8" baking pan with parchment paper; grease parchment paper with nonstick cooking spray and set aside.
Heat cream, sugar, syrup, and honey in a 6-inch diameter 2-quart saucepan over medium heat; stir until sugar dissolves, about 5 minutes. Bring to a boil and attach a candy thermometer to the side of the pan; cook, without stirring, until mixture reaches 250°F, about 45 minutes. Remove pan from the heat and add butter. Using a wooden spoon, stir until smooth, about 3 minutes.
Pour toffee mixture onto prepared baking pan and sprinkle evening with peppermint candy peices, pressing them lightly into toffee with the back of a spatula. Let cool completely; cut into 64 squares to serve.