While I’m not entirely clear on what you are asking (or what the board actually looks like, which I expect is not the same as the Fritzing PCB view), I would expect the various pads to be free of solder mask (so they can be soldered to) and the rest of the board covered in mask. If you want the entire board covered as mask, I expect you would need to do the board outline with no traces or pads, output that as a gerber, save the mask layer from that gerber output, then redo the board with the pads and traces, then replace the gerber mask layer with the saved layer from the board with no traces. The best bet would probably be to upload a photograph of the actual board with pointers to where you want to add solder mask.
Peter