Ileodictyon cibarium - Lattice or Basket Fungus; common. Just one found when raking leaves and when I bent down to touch it it popped out of it's 'egg'.
The Ileodictyon cibarium or Wrinkled Cage, which I notice is missing from the species list, has broad, transversely-wrinkled arms and are not wider at the joints. How exciting for you to have it 'pop' out of its 'egg' for you. Some gardeners get such a shock when this happens. The I. gracile or Smooth Cage, is smooth, like yours, thin and the 'arms' broaden out slightly where they join. I have yet to see a 'fresh' one of either of these!!!
Just looked at the entry in the book and I feel it's a bit deceptive as that the main image is of Ileodictyon gracile. Sorry about that. And yes they are fairly common in mulched gardens.