Your solution here would be utilizing multiple surfaces. Your first surface would be, of course, your EG. The second surface (lets call it SURFACE 2) will include only two feature lines (credit to AllenJessup and castled71049) (i.e. breaklines); one is the building outline at the finished floor elevation and the second on is the offset that represents the basement floor elevation (use a offset difference of 0.01'). The final surface (lets call it COMPOSITE SURFACE) will be a composite of the two surfaces to show the final product. Just paste the EG surface first then paste SURFACE 2. For cut and fill quantities, just compare the EG to SURFACE 2. Depending on your finished floor elevation, coutours may go through your building as your illustration shows. Like rl_jackson stated, add a hide boundary so the contours won't show.
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