It's a 'breather' hole which is open to atmosphere and allows the diaphragm in the large dia top section of the EGR valve to function correctly. The main body of valve routes airflow from the turbo into the cylinders. This air can be contaminated with oil mist from the breather system and leakage from the turbo oil seals.
I'd guess there is some wear on the EGR valve spindle which is allowing this oil mist to collect in the cavity below the diaphragm and weep out of the breather hole.
It's likely to be worse when the EGR valve is activated so as a test you could disconnect the small braided vacuum hose from 'top hat' section of the diaphragm capsule, wipe off the oil residue, and see if it stays clean.
Use a small tight fitting bolt to seal the braided hose and cap or tape off the stub pipe to prevent dirt entering the capsule.
Cheers Spike
