Lightly oil a 9x9 baking pan and set aside (you can also line the bottom of the dish with parchment paper to make removing the squares even easier.
Pour 5 cups puffed wheat and 1/2 cup dried cherries (if using)into a large bowl. Set aside.
Combine 4 Tablespoons unsalted butter, 1/2 cup corn syrup, 1/2 cup granulated sugar, 2 Tablespoons brown sugar, and 4 Tablespoons cocoa powder together in a small saucepan. Bring to a boil over medium heat (mixture must come to a boil or the syrup will not set and your squares will fall apart). Remove from heat and stir in 1/2 teaspoon vanilla extract.
Pour cocoa syrup mixture over puffed wheat. Stir until puffed wheat is completely coated. Firmly press the mixture into the prepared baking pan (but not so firmly that you feel the cereal getting crushed) and let set at room temperature for at least an hour. Cut into squares and serve, or transfer to a zipper bag or airtight container to store.
Notes
Puffed barley or kamut can be used instead of wheat if you prefer.