Generating 3D objects in illustrator is all about illusion. In your case you are trying to create a 3D object with 1 shape. However sometimes it's best to create the illusion of 1 shape or object by using two or more. For example the object below I created is two shapes, one on top of the other.
Here's how it breaks down visually.
And here is the step by step process. This process and individual steps can be applied to any object you are attempting to rending in 3D.
Step 1. Create the general shape of the object you are replicating. Apply a color stroke (8pt green in my case) and ensure the fill color is blank. The reason the fill color must be blank is because we want to be able to see through it to the next shape.
Step 2. Go to Menu > Effect > 3D > Extrude and Bevel. A new window with open.
Check the "Preview" box in the lower left corner. Then adjust the angle and perspective of the shape by dragging the 3D box. You will notice your object move accordingly. In your case, I lowered the Extrude Depth from the default 50pt to 18pt. This is the depth of our shape so we wanted something a bit more shallow.
Changing the bevel (#2) to classic changes the shape of the sides of the 3D stroke. Sometimes adjusting the bevel will give you a small notice (#3) that the bevel intersected with it's self. This means the bevel crossed into itself and may look "wonky", I usually look for break down in the shape then move on, as in this case.
You will also notice that because we did not have a fill color (#3) we are able to see the inside walls of the object.
Step 3. Duplicate the object then press
Shift + X. This will switch the stroke color and the fill color. Because we did not have a fill color, the new object will have a fill color and no stroke color. Opposite the original object. This new object is the "base". Ensure the new object is behind the first object.
Ctrl + [ to move it backwards.
Step 4. Now I set the extrude level of the new object to 0. Press
Shift + F6 to access the appearance window. Then click 3D Extrude and Bevel. Keep in mind you can also use this to adjust the original objects options too.
I added a slight gradient color and inner glow to the object to make it a bit more believable. You add the inner glow by clicking the "fx" icon in the appearance window.
Step 5. Drag the new shape into position behind the first object. Sometimes just centering it on the top object will work however this may not always be the case depending on the shape you are using.
Hope this helps.