The "stud with a nut" is an adjustment point. It is to adjust the interface spacing between the booster and M/C. There should be around 1/16" gap at rest between the "stud" end and the contact point on the M/C. Too small a gap and the brakes will drag, too large and you will have excessive pedal drop before brake engagement. The actual adjustment is hard to do because of the socket in the M/C where the ball goes. But there is a cheap tool to help you. It looks like a sheetmeat 'H' with a movable rod thru the crossbar in the 'H'. With that said, normal pedal adjustment is with the rod as Davis Dyehouse said.

Six volt guy living in a twelve volt world