Step 1: Decide what an ideal test for a pancreatic head cancer must do: see a small deep tumour clearly, assess vascular involvement for resectability, and obtain cells safely.
Step 2: $EUS$ wins on every count. From inside the duodenum the transducer sits millimetres from the lesion, detecting tumours other modalities miss, and EUS-FNA delivers a diagnosis through a low-risk route compared with percutaneous needles.
Step 3: Compare alternatives. ERCP is best for relieving obstructive jaundice and brushing the duct, not for staging. A percutaneous guided biopsy carries needle-tract seeding risk and does not stage the disease.
Step 4: Transduodenal or transperitoneal sampling is invasive and risks tumour spillage. So, paired with CT for distant staging, EUS is the single best investigation for carcinoma of the head of the pancreas.
\[\boxed{\text{EUS}}\]