Hi W - recipe is quite exact in'it..... - take the pork from the pot and add the onions and other stuff......so yes cook in the fat from the meat.
What it fails to state is that you should make sure you de-glaze the base of the pot to get all the sticky bits off the bottom of the pot to add to the stew - flavour is in all those little bits of onion, meat and stock that gets to caramalise on the base, so do make sure these get into the liqor too. JO does say '..give it a little shake..' yeah ok, I'll shake a full cooking pan too......
And watch the amont of smoked paprika - it is quite strong stuff - even the 'mild' version and will overpower every other flavour, so less rather than more for caution.
Make your own sour cream too - add a few drops of lemon juice into a pot of single cream and leave at room temp for 30 mins. Half the cost and just as nice. Or use a yoghurt instead to thicken and add gloss.
If you want to make a thicker sauce than that from just the tew, take some of the cooking liqor out when ready to serve, just reduce the liquid to concentrate the flavours and if still too thin, thicken with cornstarch.
Try serving with spaetzle dumplings for a proper Hungarian job, or a creamy celeraic mash, or over noodles as an option too. Or try with a red rice which is a nice nutty flavour to go with the stew.
Hope it goes ok!