Step 1: Identify the metabolic bone disease whose hallmark on plain films is a thickened bony border framing the vertebral body. That disease is Paget's disease, driven by overactive osteoclasts and compensatory osteoblastic bone laying.
Step 2: During the bone-forming stage, the cortex and both end plates of an affected vertebra become densely thickened while the central trabeculae remain coarser and relatively lucent. The outlined square produced is termed the picture frame vertebra.
Step 3: The same disease can turn a whole vertebra uniformly white (ivory vertebra) and produces the blade-of-grass lytic front in long bones plus cotton wool patches in the skull.
Step 4: Excluding others: osteopetrosis gives the sandwich or rugger-jersey spine, simple osteoporosis empties the body leaving a faint cortex, and ankylosing spondylitis squares the corners and bridges with syndesmophytes. So the picture frame vertebra belongs to Paget's disease.
\[\boxed{\text{Paget's disease}}\]