Although the cap and gills do look remarkably similar to that of shiitake, the persistent ring on the stem indicates that you probably have a lookalike species. Typically, the veil on a shiitake mushroom will disappear when they expand, not leaving behind a ring on the stem. The stems are also fibrous and darken as they age.
Also, I have been growing shiitake for 30 years now and I've never seen them grow on wood chips in a garden. Shiitake is
native to Japan, Korea and China, where they are found on dead and dying
trees, logs and tree stumps. A few wild "escaped" populations have been found in Wisconsin, California and Washington, however. But my gut feeling is that you probably have something else.