I've never actually thought of chucking the fat in the food processor, mainly because I thought it would get clogged and burn the motor out or something (this kind of thing often happens to me!).
Currently, I'm using a hand-cranked cheapo mincer, which is made from some kind of composite material and suckered to my worktop (it's come unstuck a few times and gone flying). I've noticed that the auger squeezes the fat so intensely that the sub-structure of it breaks down and then it's extruded into the usual mince profile. Ultimately, I throw this minced product into a large glass jar, which I submerge in a pan of simmering water. Apparently, the squeezed/extruded fat is more fractionated, so it melts very quickly and easily and I simply pour the liquid (not hot, just enough to melt) through a sieve/strainer to remove the undesirables. I'm then left with a product without its non-fat bits that's compactly stored and easily accessible for re-melting or thinly slicing (like a block of cheese) - akin to rendered, but of course, sub-violently-thermodynamic prepared.
I find that auger+extrusion mincing facilitates this melting method - does the food processor method allow the same end product?
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Also, I've backheeled suet recently in my search for a nicer fat, which is more like cream/butter and gladly, I've discovered a fat cut that's creamier and with more of a yellow tinge. My farm/butcher calls this fat "top brisket fat", which usually comes in cuts almost as long and slender as my arm. Personally, I find this fat to be (consistently!)the creamiest and most delicious fat of all - has everyone tried this fat, with mixed opinions (given that it seems to have a relegated position alongside suet)?
Maybe this is the "back fat" that RawZi was referring to (I think I used to go in the shop and initially ask for "back fat", which is a term I borrowed from Fat of the Land, but they never knew what I meant)...In that case, if you're in the UK, simply ask for "top brisket fat" (I can usually secure up to 1.5kg per week).
Just my two penneth/cents...;-))