A 38-year-old woman with newly diagnosed type 2 diabetes mellitus (fasting glucose 186 mg/dL, HbA1c 9.2%) is started on a sulfonylurea. After 2 weeks, she reports severe hypoglycemic episodes (blood glucose 42 mg/dL) despite dietary compliance. Which investigation would best determine whether her hypoglycemia is due to an excessive insulin secretory response to the drug or an underlying insulinoma?