Database

[{"_id":ObjectId("5ceb7e71636566fe7718733e"),"project_name":"p1","expected":"19-Sep-2019","actual":"19-Sep-2019"},{"_id":ObjectId("5ceb7e71636566fe77187340"),"project_name":"p2","expected":"20-Sep-2019","actual":"20-Sep-2019"},{"_id":ObjectId("5ceb7e71636566fe77187342"),"project_name":"p3","expected":"19-Jan-2020","actual":"19-Jan-2020"},{"_id":ObjectId("5ceb7e71636566fe77187344"),"project_name":"p4","expected":"20-Jan-2020","actual":"20-Jan-2020"}]

Query

db.collection.aggregate([{$addFields:{months:["","Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"]}},{$addFields:{date:{$dateFromParts:{year:{$toInt:{$substr:["$expected",7,4]}},month:{$indexOfArray:["$months",{$substr:["$expected",3,3]}]},day:{$toInt:{$substr:["$expected",0,2]}}}}}},{$match:{date:{$gte:ISODate("2019-09-01"),$lte:ISODate("2019-09-30")}}},{$unset:["months","date"]}])

Result