2010 knocking after sitting

The terminology you're using, presumably passed on from the mechanic, isn't that clear. Here's the components. The terminology is not quite kosher, per Toyota, but it's clear and succinct.

The EGR Cooler:



The EGR Valve:



The EGR Pipe:



The EGR pipe is easy to access/remove, and completely trivial to clean. The EGR valve is more difficult to remove, typically it comes off together with the cooler, and cleaning is a little harder, but not bad.

The EGR cooler is the bear: can clog up with carbon in the internal radiator fins, takes time and patience to clean. Following advice here, I cleaned mine with multiple soaks of strong Oxi-Clean solution, came out like new.

And the last portion of the EGR circuit is the passages in the intake manifold, from the EGR pipe connection to the intake ports. That last portion in particular is trouble prone, they're small diameter passages, one per port:



Addendum: shuffled the components so they're in the order of "flow", per @Rebound post.

 

So you see, looking at Mendel’s illustration, that exhaust gas flows into the EGR valve and cooler, through the EGR pipe, and into the intake manifold. It ALL gets gunked up.

A second cause of contamination is the PCV valve, which also feeds into the bottom intake manifold. These definitely allow oil into the intake manifold, which causes problems over time. At a minimum, it all needs to be cleaned out. As a more major step, some owners install a third-party “oil catch can,” between the PCV valve and intake manifold. These things catch the oil before it enters the crankcase — and they work! But they need to be emptied at each oil change, and of course they need to be installed.