Database

[{_id:1,user_id:10,line_items:[{_id:2,quantity:2,},{_id:3,quantity:1,}],purchase_date:"2021-02-05T21:00:00.000+00:00"},{_id:2,user_id:10,line_items:[{_id:2,quantity:2,},{_id:3,quantity:1,}],purchase_date:"2021-03-05T21:00:00.000+00:00"},{_id:3,user_id:10,line_items:[{_id:2,quantity:2,},{_id:3,quantity:1,}],purchase_date:"2021-04-05T21:00:00.000+00:00"},]

Query

db.collection.aggregate([{$group:{_id:{"$substr":["$purchase_date",0,7]},count:{$sum:1}}}])

Result