Askanazy cells are microscopic findings in
HASHIMOTO'S THYROIDITIS (Struma Lymphomatosa) 

Also called as diffuse non-goitrous thyroiditis. 
It is an autoimmune thyroiditis—common in women (15 times more common). 
There is hyperplasia initially, then fibrosis, eventually infiltration with plasma cells and lymphocytic cells. 
Askanazy cells are typical (like Hurthle cells). 
The river Struma arises in Bulgaria and flows into Aegean Sea. 
Struma means goitre. Banks of this river are endemic area for goitre. 

Key Concept:

Hashimoto’s thyroiditis is an autoimmune thyroiditis—common in women (15 times more common).
There is hyperplasia initially, then fibrosis, eventually infiltration with plasma cells and lymphocytic cells. Askanazy cells are typical (like Hurthle cells).

​Reference: SRB's Manual of Surgery, 5th ed, page no 436
De Quervain's thyroiditis
Riedel's thyroiditis
Hashimoto’s thyroiditis
None of the above