Here is more recent info and it appears that the technology has been made better. But going back to one of my original statements , the main technology being used is E. Coli although mouse cell is better it is still breaking out or emerging. So using the E. Coli method as you can read below sounds pretty extensive for just anyone to do it.
Inclusion Body Technology
The first method of manufacturing rHGH was called inclusion body technology. In this process E. coli bacteria mass produce rHGH, which accumulates in small bodies inside the bacteria. These small bodies are isolated and the highly enriched rHGH is separated and purified. The rHGH produced by this technology differs by one extra amino acid at the end of the protein. Although this rHGH was an improvement to cadaver derived growth hormone, the extra amino acid caused an allergic reaction in some people.
Protein Secretion Technology
As of 2010, a newer technology is used to manufacture most currently available rHGHs on the market. It is referred to as protein secretion technology, and its major advantage is that rHGH is secreted from E. coli and does not accumulate in inclusion bodies. This process allows for easier purification of rHGH and the production of rHGH that is identical to human growth hormone.
Mouse-Cell Technology
Producing rHGH using mouse-cell technology involves insertion of the DNA that encodes for human growth hormone into the DNA in mouse cells. The protein is produced in mouse cells instead of E. coli bacteria in the laboratory. Although more costly initially, this process produces rHGH that requires less manipulation and purification. This technology also produces rHGH that is identical to human growth hormone.