Nidula candida or Crucibulum sp?
Bird's Nest Fungus that produces a number of lens-shaped eggs (peridioles) that may or may not be attached to the inside of the cup. The spores are produced inside the peridiole, more or less like a puffball. Inside each cup, which is enclosed by a cover until maturity, the peridioles develop in a glutinous matrix. At maturity, the cover falls away and allows falling raindrops to splash the peridioles out of the cup and onto the surrounding substrate. Eventually the peridioles break down and the spores are released. Cyathus has a thin, thread-like cord which remains attached to each peridiole. Nidula has no threads attaching the peridioles and Crucibulum have a short cord which sometimes leaves a stub attached to the peridiole when it leaves the cup.
Composted manure with sawdust in it, used as a mulch on my garden last summer. There are lots of fungus in it this spring!
I am not totally sure which species I have here. Does anyone know? It doesn't look like Cyathus striatus at all, but I think those are little cords (photo 1) attaching the peridioles to the cap. Photo 4 shows a developing cup that is still covered.