If you just restrict the inlet manifold side (the rectangular one with four holes, one in each corner) you will obviously increase the build-up of soot in the EGR valve, as the oval entrance isn't restricted (the exhaust fumes will pour into the unrestricted EGR, but will be restricted in the EGR due to the inlet manifold restrictor gasket).
This isn't really correct. The massflow into the valve will be exactly the same as the massflow out of the valve and it's the massflow that's important because the quantity of soot particles will be in proportion to this. The flow can't "back up" around the valve when there is only one gasket fitted on the manifold side because massflow in, through and out remains constant regardless. Fitting the second restrictor plate at the inlet to the valve will simply reduce the massflow though the valve more than having just the 1 plate fitted.
It's possible the plate was fitted on the EGR inlet to increase the velocity of the flow entering the valve to provide some "blast" cleaning affect.
Having said that the fundamental problem with these valves isn't related to the fact they have a bit of soot in the flow path it's related to the fact the soot makes it's way past the actuating rod into the chamber above the valve head where the spring mechanism sits. This gets clogged with soot which eventually prevents the spring returning properly leaving the valve partially jammed open. It isn't even clear if the restrictor plates were fitted to resolve issues with the EGR failing, contamination of the inlet manifold or simply to improve performance.