Steam the broccoli florets in a steamer basket until they become tender. If a steamer basket is not available, boil the broccoli in water until softened.
Transfer the cooked broccoli to a large mixing bowl. Mash it thoroughly with a fork until it becomes roughly pureed with a soft, broken-down texture.
Add the minced chicken, egg, shredded cheese, panko breadcrumbs, and garlic powder to the mashed broccoli.
Mix the ingredients together until the mixture is evenly combined and holds together as the nugget base.
Moisten your hands with water, then take small portions of the mixture and form them into nugget shapes.
Shape approximately 12 nuggets, adjusting the size as preferred, and place them on a baking tray lined with baking paper.
Heat a small amount of olive oil in a pan over medium heat.
Place the nuggets in the pan and cook until each side becomes deeply golden brown and crisp on the outside.
Serve the nuggets warm on their own or alongside a suitable sauce, fruit, vegetables, or other snacks.