In a bowl, mix together the chopped broccoli, grated carrot, cheese, and breadcrumbs.
Add the egg and mix until everything is well combined. If the mixture feels too wet, add a bit more breadcrumbs.
Heat a little oil in a pan over medium heat.
Scoop about 1–2 tablespoons of mixture and flatten into small fritters in the pan.
Cook for about 3–4 minutes per side, or until golden brown and cooked through.
Let cool slightly before serving to your toddler.