Add 1/4 cup of panko breadcrumbs, milk, salt, garlic powder, onion powder, and paprika to a small bowl and mix it together until combined. Let it sit for about 1 minute so that the breadcrumbs can absorb the liquid. This mixture is called a panade.
Add the soaked breadcrumb mixture (panade) to a large bowl along with the ground chicken breast and mix until well combined. Use your hands as needed to make sure everything is well incorporated, but try not to overmix.
Place the chicken mixture on a parchment paper lined baking pan (I used a 9-inch by 13-inch baking sheet) and smooth it out into an even layer that is about 1/2 inch thick. Place another sheet of parchment paper on top of the chicken layer and gently smooth it with your hands. Place this sheet pan in the freezer for 60 to 90 minutes to allow the chicken to firm up.
Once the chicken layer is firm, peel away the top parchment paper layer and use dinosaur-shaped cutters to cut out dino shapes from the chicken. Cut out as many shapes as you can and place the dino cutouts aside on a separate parchment paper-lined pan. You can either repeat the process of smoothing out the scraps into an even layer to cut out more dino shapes, or you can use the scraps to form normal round chicken nuggets. If your dino chicken cutouts seem soft, place them back in the freezer to firm up for a few minutes before you start coating them. You want the chicken pieces to be firm so that the shape isn't distorted when dipping.
Preheat the oven to 375 degrees. Mix together 1 cup of panko breadcrumbs, parmesan cheese, flour, and 1/2 teaspoon of paprika together in a medium bowl until combined to form the breading mixture. In a separate bowl, whisk the two eggs.
Dip each dino nugget cut out into the breading mixture, then into the whisked egg, and then back into the breading mixture to fully coat. There won't be much coating that sticks to the nuggets during the first dip, and that is perfectly fine! The first dip is to help the egg stick to the nuggets and the remaining breading will stick during the next pass. Repeat for the remaining nuggets and place them back onto the parchment paper-lined pan.
Spray a generous amount of cooking oil on top of the nuggets (don't forget this step because this is what helps the nuggets get nice and crispy)! Bake the nuggets for 15 to 18 minutes, flipping halfway through, or until the nuggets are crispy and golden. Let them fully cool before serving.