Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a large pot of boiling water, cook the broccoli florets for 2-3 minutes, or until tender-crisp. Drain well and let cool slightly.
In a food processor or blender, puree the cooked broccoli florets until finely chopped. Alternatively, you can mash them with a fork.
In a large bowl, combine the puréed broccoli, shredded cheddar cheese, whole wheat flour, and egg. Mix well until a dough forms.
Roll tablespoons of dough into balls and place them on the prepared baking sheet.
Gently flatten the balls slightly with a fork to create a bite-sized shape.
Bake for 10-12 minutes, or until golden brown and set.
Let the bites cool completely before serving them to your dog.