[{likes:[{like:true,username:"bob"},{like:false,username:"tim"}]}]

db.collection.aggregate([{"$project":{"likes":1,"likesAux":{"$filter":{"input":"$likes","as":"l","cond":{"$eq":["$$l.like",true]}}}}},{"$set":{"likeCount":{$size:"$likesAux"}}},{"$project":{"likesAux":0}}])