Step 1: Recall the Leloir pathway, which converts galactose into glucose-1-phosphate through three enzymes: galactokinase, galactose-1-phosphate uridyltransferase, and UDP-galactose epimerase.
Step 2: Classic galactosemia, the severe disease presenting in neonates, maps to a block at the middle step, the transferase $GALT$. This is the answer the question targets.
Step 3: Loss of $GALT$ traps galactose-1-phosphate, which poisons liver, brain and kidney, while diverted galactose forms galactitol that clouds the lens and causes cataracts.
Step 4: Separate the look-alikes: galactokinase deficiency is a milder, mainly cataract phenotype, epimerase deficiency is a rarer variant, and HGPRT is a purine salvage enzyme that has nothing to do with galactose.
\[\boxed{\text{Galactose-1-phosphate uridyltransferase}}\]