Assume you have a food item that you have determined is Bishul Akum. If you cut that food item with a knife, do you have to wash that knife before using it on your other food?
There's a dispute (Shu"a Yo"d 113; 16) whether Bishul Akum requires the vessels used, to be Kashered or not. Better to follow the strict opinion (Rashba) when possible. If your knife cuts a cold Bishul Akum – wash it off and you can use the knife right away. If you're cutting a hot piece in a plate – there're more grounds to be lenient since according to some opinions food in Kli Sheni doesn't cook even when hot. If you are cutting a hot piece of Bishul Akum in a Kli Rishon – the above applies – better to Kasher but can relay on lenient opinion (Rosh)