Congratulations, Mspence! Your "heavy brass" (actually, copper) find is a rare INTACT civil war Confederate 3"-caliber artillery projectile's disc-sabot, specifically known as a Tennessee sabot or Mullane sabot. It was held onto the projectile's base by a heavy bolt in the center, and three iron studs which fit through the three holes in the disc. (See the photos below).
Usually these disc sabots are torn by firing-blast... and the shells are almost always found with the disc-sabot missing. Yours is definitely fired, but amazingly, still completely intact and undamaged, except for a little splitting at the stud-holes' edges.
Your intact one could be used to replace a missing one from somebody's unexploded Tennessee/Mullane shell, which makes your find worth about $150 (retail).
The copper-disc-sabot in the photos is unfired, so it has its original "saucer" curvature. Yours was flattened by firing-blast, which is how the disc-sabot "works" to grab the cannon's rifling-grooves.
The dark object at the center of the sabot in photo #3 is the remnants of the wooden "doughnut" which helped to partially protect the sabot from firing-blast damage.