For patients with essential thrombocythemia already on prophylactic dose DOACs, do you defer starting aspirin?  

I usually defer aspirin in these situations. There is evidence from PV that aspirin plus anticoagulation increases bleeding risk (Zwicker et al., PMID 34162181). If an ET patient has a high-risk disease with prior arterial thrombosis, then I would favor adding aspirin. 

I agree with Dr. @Tremblay. Occasionally, patients have microcirculatory symptoms off aspirin and for those patients, both DOAC and aspirin are given, but as Dr. Tremblay mentioned, that is associated with increased bleeding risk.