The “birdseye” structures are oncolites (also called algal balls, or algal concretions). These are typically formed when layers of calcium carbonate precipitate around a nucleus (sometimes a shell, twig, or other particle), with layering driven by algae or microbial activity in a lake environment.

Because of this, you’ll see small rounded or oval concentric forms in cross-section which make it visually striking

The stone polishes very well (hence its “marble” use) and has been used in prominent buildings.
Historical Metabolic Database

In the Utah State Capitol, the “Gold Room” walls are adorned with this Birdseye marble.
Utah Geological Survey

It’s also reported to have been used in the Mormon Chapel in Washington, D.C., the Lincoln Memorial, and other state and federal buildings (though these attributions are less well documented in formal geological sources, they show up in local/historic sources).