Can mobs spawn on slabs?

Endermen are dismantling my mob grinder.

This question has an answer that suggests endermen can't spawn on slabs, so if I cover the whole floor with slabs, I should be fine. Except I read single slabs are considered "transparent" and monsters can only spawn on "opaque". OTOH, double slabs are considered "opaque"... how does that relate to monster spawning?

Mobs cannot spawn on normal, right-side-up single slabs (the ones occupying the lower half of the block), as they're considered transparent blocks. They can spawn on upside-down single slabs (as of the 1.5 update) and double-slabs (which are full, opaque blocks).

Flooring your grinder with regular half-slabs will prevent all mobs from spawning, not just endermen.

No, mobs cannot spawn on single slabs. This wiki article explains in detail the requirements for any given mob to spawn.

To prevent endermen from making holes in your grinder, make the spawning level only 2 blocks high, or set mobGriefing to false.