From National Geographic:
It's called prelamination: Tissue that's going to be used to rebuild an area is constructed in multiple layers.
Take the nose, for example. If the damage from disease or injury goes all the way through, then all three layers must be replaced: the skin on the outside, the cartilage, and the soft lining inside. The forehead skin tends to be the best match for the outside skin from an area called the paramedian forehead flap...
It's not "grown" on the forehead, but rather, "constructed". While the nose is being constructed on the forehead, it does not get connected to the normal air passages. After the nose is constructed, it is moved to its final destination where a nose normally would go, and connected with the normal air passages.
This technique also been performed using the forearm (Sinha et al. 2008) (includes pictures of the procedure). They also say that "a forehead flap, traditionally, has been the workhorse of such reconstructions and can provide excellent nasal reconstruction", but that "an adherent forehead scar precluded the use of a forehead flap".
The standard technique (using the forehead) is described in (Menick 2008, at p. 329).
Menick, Frederick J. Nasal reconstruction: art and practice. Elsevier Health Sciences, 2008.
Sinha, M., J. R. Scott, and S. B. Watson. "Prelaminated free radial forearm flap for a total nasal reconstruction." Journal of Plastic, Reconstructive & Aesthetic Surgery 61, no. 8 (2008): 953-957.