[{a:1,"mostImportant":"qwer","lessImportant":"rty"},{a:2,"lessImportant":"weRt","notImportant":"asd",},{a:3,"mostImportant":"qwe2","notImportant":"asd",}]

db.collection.aggregate([{$project:{"a":1,lessImportant:1}},{"$addFields":{"attrToSearch":"..."}},{"$match":{attrToSearch:{$regex:"wer",$options:"i"}}}])