In Denmark we usually do not have dishwashers of the automatic persuasion. We have the elbow grease kind. (More and more homes are getting dishwashers... but it's not going to happen in this home any time soon.) So this advice is only relevant to those who are still doing their dishes the archaic way: by hand with a scrub brush in a bowl of hot soapy water.
Have you ever had the problem where after washing a dish that was, say heavy on the cheese that you get melted cheese in your brush and you can JUST NOT GET IT OFF? I would then throw away the brush and get a new one, grumbling loudly. But then it came about that I was eating these cheesy dishes more frequently than I wanted to buy new brushes. I don't like to throw them away. Yeah, they're cheap, but they're also plastic and they'll never break down in the dump!! In the days of yore, when I had a dishwasher, I could just throw the brush into the dishwasher and the magic soap would dissolve it. But that didn't happen with the liquid soap here. And since we have no dishwasher, we obviously have no dishwasher soap.
Enter husband. Husband says, "try laundry soap." Exit husband.
It works! By golly it works! I had Penne a la Vodka last night from the Pioneer Woman and it left a bit of a cheesy mess. Dumped some laundry detergent in the pot along with my scrub brush and the eating and serving utensils and watched a Dr. Who episode (To be Continued??? NOOOOOOO!!!!) before going back and finding a miraculously clean pot et al.
I don't know where the cheese goes. It's magic.
This also works on the baked-on grease on oven dishes and any and all egg problems (what you've never glued bread to a pan with egg? Oh, it's just me then? Never mind).