Epicarp and seed of Hass avocado (Persea americana Mill.) are agro-industrial residues rich in bioactive compounds. In this study, a pressurized liquid extraction (PLE) method was optimized to obtain phenolic compound-rich extracts with neuroprotective potential. The optimal extracts, obtained from 100% epicarp with pure water (0% ethanol) at 40 °C and 100 bar, demonstrated high extraction yield (26.8 ± 0.9%) and total phenol content (TPC = 505 ± 25 mg gallic acid equivalent/g dry extract), good antioxidant capacity (ABTS = 3350 ± 179 µmol Trolox equivalent/g dry extract, ORAC = 0.14 ± 0.01 µg/mL), and moderate acetylcholinesterase inhibition (33.6 ± 2.9 µg/mL). UHPLC-ESI-QTOF-MS analysis of the optimal extracts tentatively identified phenolic acids, phenolic alcohol derivatives, and various flavonoids; namely flavonols. The results reveal the potential of avocado processing by-products, particularly the epicarp, as source of potential neuroprotective agents. The proposed PLE methodology was demonstrated to be a sustainable and efficient strategy for avocado residues valorization.