MVC EditorTemplate using jQuery UI DatePicker not working for nullable date fields

Question

Long ago I found out the best way to attach a DatePicker to a date field is to use the EditorTemplate DateTime.cshtml:

@model DateTime?
@Html.TextBox("", (Model.HasValue ? Model.Value.ToShortDateString() : string.Empty), new { @class = "datePicker" })

And in jQuery script:

$(function() {
        $(".datePicker")
            .datepicker({ showOn: 'both', dateFormat: 'dd/mm/yy', changeMonth: true, changeYear: true })
            .next('button.ui-datepicker-trigger')
            .attr("tabIndex", "-1");

        $('.page').offset({ top: 10 });
    });

It always worked before but now I am using VS 2015 and MVC5 I am finding that it works for this field;

public System.DateTime GivenDate { get; set; }

but not this one which is nullable:

public Nullable<System.DateTime> StartDate { get; set; }

In IE developer tools I find the markup transforms from

@Html.EditorFor(model => model.contract.GivenDate)
@Html.EditorFor(model => model.contract.StartDate)

to

<input name="contract.GivenDate" class="datePicker hasDatepicker" id="contract_GivenDate" type="text" value="">
<input name="contract.StartDate" class="text-box single-line" id="contract_StartDate" type="date" value="">