A "nasty deli" is a sexual manuver in which a man enters a deli and notices a hot young lady working in the back on the grill. He then makes his way behind the counter and bends her over the grill and starts fucking her in the ass from behind. Then he hears something sizzling on the grill and it turns out to be the girls balls because shes really a dude.
WHAT THE FUCK?!? You're a dude? This is a nasty deli.