Decorative eggs can be made from any substance under the sun. Metal eggs exist, but appear to be less common than those made of other materials.
A simple brass egg is pictured below; it is a souvenir of Turkey, and screws open to reveal a secret storage compartment. As is common in many Muslim cultures, calligraphy is used for decorative purposes on the surface of this egg.
The other eggs harken from China, and are created by the process of Cloisonné, an ancient metalworking technique. Cloisonné is a multi-step enamel process used to produce jewelry, vases, and other decorative items, which first developed in the Near East. It spread to the Byzantine Empire and from there along the Silk Road to China, now the site of many high quality production facilities.
Cloisonné (According to Wikipedia)is created in a multi step process:
First, the artist forms metal (such as copper or brass) into the shape of the finished object.
A paper pattern and a pencil are used to transfer a design to the metal object.
Partitions (French: cloisons) that act as color-separators are applied according to the
transferred pattern and are held in place by a soldering paste (this is finely divided metal of
low melting temperature in a flux paste). The partitions are bent and cut to length from flat
wire stock (usually by hand using simple pliers) while the paste is applied with a small
brush.
Heating the piece in an oven permanently affixes the partitions to the base metal by melting
the solder. The piece is then allowed to cool.
Frit (glass crushed to a powder) in a water-based paste is painted into the partitions using
an annotated pattern similar to the "paint by numbers" craft technique. After the frit has
dried, firing in an oven melts it onto the metal. Several repetitions of the process may
ensue to build up the coatings to the height of the partitions. Various colors and
transparencies may be used in combination within a single partition to obtain the desired
artistic effect.
The glass and a portion of the cloisons are ground and polished to form an even and smooth surface.
The exposed metal is electroplated with a thin film of gold to prevent corrosion and to give
a pleasing appearance.
The end result can be seen in the lovely Chinese eggs below.