The current study aimed at developing an effective organosolv treatment, with the objective to obtain potato peel extracts highly enriched in polyphenols. To this end, two low-cost solvents were employed, 1- and 2-propanol, which are considered green, but they have been rather poorly studied compared to other conventional solvents, such as ethanol. Treatment development also embraced the use of sulfuric acid, a well-examined catalyst in organosolv processes. Treatment evaluation on the basis of response surface optimization and severity demonstrated that 1-propanol was a more effective solvent, providing a maximum yield in total polyphenols of 19.28 mg chlorogenic acid equivalents per g of dry potato peel weight, attained with 40% 1-propanol/1.5% (w/v) sulfuric acid at a treatment time of 60 min and a temperature of 90 °C. This treatment was of lower severity compared to the one with 2-propanol, and it also provided almost 24% higher total polyphenol yield. The extracts produced contained chlorogenic acid as the major constituent, accompanied by caffeic acid and minor amounts of p-coumaric acid. This is the first report on such an organosolv treatment of potato peels to recover polyphenolic compounds with high efficiency.