Place eggs in large saucepan or deep frying pan of cold water. Bring to a boil over med-high heat, STIRRING GENTLY AND CONSTANTLY, *because this keeps the yolks in the center as the yolks are heavier than the whites.
Boil and gently stir for 2 minutes. Place on tight fitting lid and turn off heat. Let sit for 30-35 minutes. (Depending on how large your eggs are.)
Carefully put eggs into bowl of ice water. Let sit for 5-10 minutes. Carefully peel eggs. (*This is easy if eggs are older. As eggs age, they shrink slightly inside. So when you boil them, you have a little room between the membrane to peel them easier.) Rinse with cold water to remove any tiny pieces of remaining shell, place on paper towel.
Slice thin slice off bottom (large end)of each egg, *this will ensure they stand up later. With paring knife, cut top third of egg off in a zig-zag pattern. CAREFULLY remove tops. CAREFULLY scoop out yolks. *Take your time doing this, you may need to use your paring knife to break up yolks inside to get them out. Place yolks in mixing bowl, mash WELL with fork. Stir in rest of ingredients except olives and peppers. Overfill bottom egg white "shell" with filling, place top "shell" on carefully pressing very gently. Place on olive slices for "eyes", pressing them into the exposed filling gently. Push 2 triangles of red pepper (or carrot) into filling to make "beak". ***You may want to boil a few extra eggs for this, in case some of them don't peel well or get wrecked, it happens. Also so that you will have plenty of filling, too! If you boil extra eggs and add the yolks to the filling, just add a bit more of the ingredients to compensate, it'll be fine! ;)