Hi SN. My method has been a combination of a strimmer with saw-blade attached (a decent sized strimmer is recommended for saw-blades - mine's a 40cc) and a 3PL box-blade mounted ont' small tractor. A pole chain-saw would be just as good as bladed-strimmer: anything that doesn't involve getting in too close for comfort!
I have used strimmer/blade 1st if gorse is really mature and then gone in to rip out stumps/roots with the box-blade tines. The latter means that the turf is churned up which, in your case, will further reduce grazing availability for a while and, of course, you would need means of restoring the churned areas for grazing. That said, I seem to think gorse does not like hard pruning (down to the ground) and it may well be that the roots can be left to eventually rot away: not absolutely certain about that, but if they do re-sprout, a topper or flail mower or even a line-strimmer could be used to check any regrowth as it appears (and the roots will eventually die as a result).
If existing gorse trunks not too thick already, a simple pass with tractor/flail mower (or similar) might be viable. If well mature, you could alternatively get in a "digger" perhaps to up-root the gorse and sort-of level out disturbed areas after the up-rooting.
And then the getting rid of arisings: from my experience, gorse "leaves" burn readily, but gorse wood needs to be quite dry to burn well.