Add your chicken breast to a pot of lightly salted water or a skillet with a splash of oil. Cook it over medium heat until it's fully done and no longer pink in the center. Let it cool slightly before moving on to the next step.
Transfer the cooked chicken into a food processor along with the eggs, softened butter, garlic powder, onion powder, and salt. Pulse everything together until the mixture turns smooth and moldable, almost like soft dough.
Scoop out small portions of the mixture and shape them into nugget shapes, or get playful with stars, dinosaurs, or circles using cookie cutters. Since the texture is so soft at this stage, shaping is quick and genuinely fun to do with kids.
Roll each shaped nugget gently in breadcrumbs until fully coated on all sides. Place them on a parchment-lined baking sheet, leaving a little space between each one so they bake evenly.
Brush the tops lightly with olive oil or melted butter, then bake at 400°F for about 18 to 20 minutes, flipping halfway through. Pull them out once they're golden brown and crisp on the outside.