I am amazed that you managed to "look up" recipes for Chicken Gordon Blue, when the dish is actually Chicken Cordon Bleu. But, that's neither here nor there.
There is a three-step method to successfully breading anything breadable, including Chicken Gordon Blue.
Step 1, dredge in flour to dry the outside area thoroughly. Breading will not stick to wet meat, even if there's just one barely damp spot.
Step 2, dip it in either straight egg, beaten, or egg and milk beaten together. This is the binding agent.
Step 3, roll it in the bread crumbs, ensuring that the item is completely coated.
Then you can choose to either deep fry, pan fry, or bake whatever you just breaded. Fried items will be moister than the baked equivalent, especially chicken breasts which are pretty low in fat content, but the mositure is from the frying oil, so baking would make the item a bit drier, but also lower in calories and fat.