We report a hafnium-containing MOF, hcp UiO-67(Hf), which is a ligand-deficient layered analogue of the face-centered cubic fcu UiO-67(Hf). hcp UiO-67 accommodates its lower ligand:metal ratio compared to fcu UiO-67 through a new structural mechanism: the formation of a condensed "double cluster" (Hf$\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$O$\mathrm{<mrow\; data-mjx-texclass="ORD">8</mrow>}$(OH)$\mathrm{<mrow\; data-mjx-texclass="ORD">14</mrow>}$), analogous to the condensation of coordination polyhedra in oxide frameworks. In oxide frameworks, variable stoichiometry can lead to more complex defect structures, e.g., crystallographic shear planes or modules with differing compositions, which can be the source of further chemical reactivity; likewise, the layered hcp UiO-67 can react further to reversibly form a two-dimensional metal-organic framework, hxl UiO-67. Both three-dimensional hcp UiO-67 and two-dimensional hxl UiO-67 can be delaminated to form metal-organic nanosheets. Delamination of hcp UiO-67 occurs through the cleavage of strong hafnium-carboxylate bonds and is effected under mild conditions, suggesting that defect-ordered MOFs could be a productive route to porous two-dimensional materials.