You would need to enable Iteration so as to permit circular references (Max Iteration set to 1) which in turn would allow you to reference the formula cell itself...
If we assume your formula is in say O19162 then
=IF(N19162="","",IF(AND(N19162>1,N(O19162)=0),TODAY(),O19162))
The date stamp in the above case would only reset if N19162 were cleared... not stipulated if that's desired or not, if you want it to persist forever more (unless formula itself deleted/re-entered) then perhaps
=IF(N(O19162),O19162,IF(N19162>1,TODAY(),""))
Most would opt to utilise VBA (Change Event) in preference to Circular Referencing.