Teenager Broadhead joined the Bucks at the start of their Evo-Stik League Northern Premier Division campaign and has featured in victories against Witton Albion and Frickley that has seen the Derbyshire club set the early pace at the top of the table.
Cook has likened the 18-year-old's four-week stint at Silverlands to that of Ryan Edwards, who is on loan with the Spireites from Blackburn.
"Jack has played two games for Buxton now," said Cook. "He has played in a 3-1 home win against Witton Albion and he was outstanding in a 1-0 win at Frickley on Wednesday night.
"He has gone out to get experience and the manager at Buxton is delighted with him, and we are delighted with him.
"Jack is going into men's football and he ticking some boxes, which will stand him in good stead.
"Jack is going to learn - like what Ryan Edwards is doing in our team. We want Jack to be doing here in 12 month's time what Ryan is doing here now. This is the progression we want for our players, we want them to be playing football."