db={MyCollectionOne:[{"firstId":"10","secondId":"123456789012345678901234"},{"firstId":"11","secondId":"999999999999999999999999"}],MyCollectionTwo:[{"_id":ObjectId("123456789012345678901234"),"otherFieldOne":"Some Data","otherFieldTwo":[{someNumber:7}]},{"_id":ObjectId("999999999999999999999999"),"otherFieldOne":"Some Other Data","otherFieldTwo":[{someNumber:9},{someNumber:39}]}]}

db.MyCollectionTwo.aggregate([{$lookup:{from:"MyCollectionOne",localField:"_id",foreignField:"secondId",as:"Temp"}},{$unwind:"$Temp"},{$match:{"Temp.firstId":"11"}},{$project:{_id:1,otherFieldOne:1,otherFieldTwo:1}}]).find()