How to increase current output of an electromagnet controller?
There is nothing on there that limits the current, it's just acting as a switch. The only limiting factor in the output current will be the failure of the FET.

The FET claims a maximum continuous drain current of 2.1A, so it should already be capable of switching a 1A electromagnet with no changes.

In the assembly as-sold, the factor that limits the current is the electromagnet itself.