**Core Concept**
The patient's presentation of recurrent cholelithiasis with a dilated common bile duct (CBD) of 1 cm suggests a possible obstruction of the bile duct. The management should focus on relieving this obstruction to prevent further complications.

**Why the Correct Answer is Right**
The presence of a dilated CBD indicates a mechanical obstruction, likely due to a gallstone. The next line of management would be to perform an endoscopic retrograde cholangiopancreatography (ERCP) or a percutaneous transhepatic cholangiography (PTC) to remove the obstruction and restore bile flow. This procedure is essential to prevent further complications such as pancreatitis, cholangitis, or recurrent cholelithiasis.

**Why Each Wrong Option is Incorrect**
**Option A:** **ERCP is not the first-line management for recurrent cholelithiasis with a dilated CBD.** While ERCP can be used to remove the obstruction, it is not the initial step in management.
**Option B:** **Percutaneous transhepatic cholangiography (PTC) is not typically used for the initial management of a dilated CBD.** PTC is usually reserved for cases where ERCP is not feasible or has failed.
**Option C:** **Surgical exploration is not the next step in management for recurrent cholelithiasis with a dilated CBD.** While surgery may be necessary in some cases, it is not the immediate next step after identifying a dilated CBD.

**Clinical Pearl / High-Yield Fact**
A dilated CBD of 1 cm or more in a patient with recurrent cholelithiasis is a red flag for possible bile duct obstruction, and prompt intervention is necessary to prevent further complications.

**Correct Answer: C.**