I found a great tip in one of Anne Watson's books! She recommends putting a small amount of dish soap (I use Dawn to cut the grease better) in each of your pots/cups/spoons, etc. before getting any water on them. Then use your gloved hands to work the dish soap into all of the oil & soap left on the utensils, around the rim of the pot, on your stick blender, etc. - all this is done before using any water!
Then you rinse everything in very hot water. Everything is ready for either the dishwasher or a quick hand washing. I can almost always be completely cleaned up in less than 10 minutes with this method.
I use a silicone spatula to scrape my soap into my mold so I don't need to wipe the pot with a paper towel. There's hardly anything left in the pot.