How to create a border gap illusion

Problem :

This is the illusion that I am attempting to create:

Notice that my designer wants the border cut off in the middle of the div, this is what I need to know how to do. I don't think overlapping with a z-index will work because of how the HTML is laid out.

This is the HTML code of which the structure may not be changed for maximum device compatibility, however, if adding an element is the solution, I believe that may be done:

<div id="nav_icons_con" class="mopn">
  <div id="inner_nav_container" class="show_inner_nav">
    <div class="nav_link_container">Home</div>
  </div>
</div>

Here is the basic current CSS code:

#nav_icons_con {
    z-index: 1;
    cursor:pointer;
    height: 5.005em;
    width: 5.005em;background-image:url(background.png);
    background-size:70%;
    background-repeat:no-repeat;
    background-position:center;
    margin:.385em .385em 0 0;
}
#nav_icons_con.mopn{
    background-color:#FFF;
    border:2px solid #83C5E6;
    border-bottom:none;
    box-shadow:5px 5px 10px #666;
}
#inner_nav_container, .inner_nav_container{
    cursor:pointer;
    display:none;
    position:absolute;
    top:5.39em;
    right:.385em;
    width:12.5em;
    white-space:normal;
    background-color:#FFF;
    border:2px solid #83C5E6;
    border-top:none;
    box-shadow:5px 5px 10px #666;
}
#inner_nav_container.show_inner_nav, .inner_nav_container.show_inner_nav{display:block;}

Solution :

The typical way to do this is to position the tab element over the sub element, so as to cover up that section of the border. However, the use of box-shadow complicates this.

One way is to add another element inside the root element, so that the root element can still cast the shadow, but the element inside is positioned above. See my code below, for a basic example.

Working Example:

.icon {
    width: 50px;
    height: 50px;
    position: relative;
    /*Create the shape for the shadow.*/
    border: 5px solid #83C5E6;
    box-shadow: 5px 5px 10px #666;
}
.icon-content {
    background: #fff;
    position: relative;
    /*Move back over the border.*/
    top: -5px;
    left: -5px;
    /*Make tall enough to cover the top border.*/
    width: 50px;
    height: 55px;
    /*Add border, except on the bottom.*/
    border: 5px solid #83C5E6;
    border-bottom: 0;
    /*Position up a layer.*/
    z-index: 1;
}
.nav {
    position: absolute;
    left: -5px;
    top: 100%;
    width: 400px;
    padding: 1em;
    background: #fff;
    border: 5px solid #83C5E6;
    box-shadow: 5px 5px 10px #666;
}

<div class="icon">
    <div class="icon-content">
        
    </div>
    <div class="nav">
        <div class="item">Home</div>
    </div>
</div>