What is this technique where they add a thick sauce and spread it out with the back of a spoon
I've seen it referred to as a tadpole or a comet but I'm not sure if either of those names are widely used. Either way, there's an excellent video on Youtube about how to do them. You want your sauce or puree to have the consistency of mayonnaise for this particular presentation. Just use a dessert spoon to place a circular blob on the plate, clean the back of the spoon and then drag the spoon back through the puree. The video is here.