If you need to do an aggregation in MongoDB on a DateTime property and you want to aggregate only by Date part, you can use a simple trick and use a filter to compose the date part before the grouping. Here is the code:

db.mycollection.aggregate(
{
    "$project" :
    {
       _id : 0,
       "datePartDay" : {"$concat" : [
           {"$substr" : [{"$dayOfMonth" : "$LastUpdate"}, 0, 2]}, "-",
           {"$substr" : [{"$month" : "$LastUpdate"}, 0, 2]}, "-",
           {"$substr" : [{"$year" : "$LastUpdate"}, 0, 4]}
      ] }
    }
},
{ "$group" :
    { "_id" : "$datePartDay", "Count" : { "$sum" : 1 } }
    }
)

Thanks to the power of aggregation framework, we can construct a pipeline where the first stage create a document with a new property that is composed only by the day-month-year. That new document can have id equal to zero if we only need a count based on that date field, or you can assign original id of the document or whatever else. The subsequent stage of the pipeline is a simple count where the id is the new field that contains only date part of the original DateTime property.