Place the Golden Oreo cookies in a food processor or blender and pulse until they become fine, even crumbs with no large pieces remaining.
Transfer the Oreo crumbs to a large mixing bowl and add the softened cream cheese.
Mix the crumbs and cream cheese together with a spatula or hand mixer until the mixture forms a thick, smooth, and uniform dough.
Line a baking sheet with parchment paper.
Scoop about 1 1/2 tablespoons of the Oreo mixture at a time, roll it between your hands, and gently shape it into a small egg.
Place each shaped egg onto the prepared parchment-lined baking sheet, spacing them slightly apart.
Refrigerate the tray of shaped eggs for 1 hour, or until the eggs are firm to the touch.
Near the end of the chilling time, place the 10 oz of white candy coating in a microwave-safe bowl.
Microwave the candy coating in 20–30 second intervals, stirring after each interval, until it is completely melted and smooth.
Remove a few chilled eggs from the refrigerator at a time to keep them firm while dipping.
Using a fork or dipping tool, lower one egg at a time into the melted white candy coating, turning to coat it completely.
Lift the coated egg out, gently tap the fork on the edge of the bowl to remove excess coating, and slide the egg back onto the parchment-lined baking sheet.
Repeat the dipping process with all of the eggs, reheating the candy coating briefly if it begins to thicken.
Allow the coated eggs to sit at room temperature or in the refrigerator until the candy coating is set and hardened.
Divide the remaining 3 oz of white candy coating into small bowls, one for each color you want to use.
Tint each portion of melted candy coating with a small amount of gel icing color, stirring until the color is fully blended.
Transfer each tinted coating to a small piping bag, zip-top bag with a tiny corner snipped, or use a small spoon for drizzling.
Drizzle, pipe, or flick the colored coatings over the coated Oreo eggs to create stripes, zigzags, or other designs.
Return the decorated eggs to the refrigerator and chill until all decorations are set and firm.
Serve chilled, or store the finished Easter Egg Oreo Cookie Balls in an airtight container in the refrigerator until ready to serve.