Step 1: Preheat oven to 350°F (175°C). Grease and flour two 8-inch round cake pans or one 9x13 inch pan. In a large bowl, combine cake mix, water, oil, and eggs. Add enough blue gel food coloring to achieve a vibrant blue color; mix until just combined.
Step 2: Pour batter into prepared pans and bake for 25-35 minutes, or until a toothpick inserted into the center comes out clean. Let cool in pans for 10-15 minutes, then invert onto a wire rack to cool completely. Once cool, use a 2.5-3 inch round cookie cutter or the mouth of your jar to cut cake circles.
Step 3: While cake cools, prepare the frosting. In a large bowl, beat softened butter until light and fluffy (2-3 minutes). Gradually add powdered sugar, mixing on low until combined, then increase speed to medium-high. Beat in vanilla extract and 3-4 tablespoons of milk/cream until smooth and creamy. Add more milk/sugar if needed for desired consistency.
Step 4: To assemble the cookie monster cake jars, place a small dollop of frosting at the bottom of each clean 8 oz jar. This helps anchor the first cake layer.
Step 5: Place one cake circle (or a layer of crumbled cake scraps) on top of the frosting in each jar.
Step 6: Pipe or spoon a layer of frosting over the cake. Break 2-3 chocolate chip cookies into pieces and gently press them into the frosting layer.
Step 7: Repeat layering: add another cake circle (or crumbled cake), another layer of frosting, and more cookie pieces. Finish with a final layer of frosting, topped with extra cookie pieces, chocolate chips, and edible googly eyes if desired.
Step 8: Chill the cookie monster cake jars for at least 30 minutes before serving. Store covered in the refrigerator for up to 3-4 days.