Place eggs in a large saucepan, cover with water, and bring to a strong simmer. Cover the pan, turn off heat, and let stand 15 minutes. Drain hot water, place pan in sink, and run cold water over eggs to cool. In a jar or other container narrow enough to keep all the eggs submerged, mix vinegar, water, salt, and pepper. Peel eggs and place in brine. Refrigerate. Pickling should be complete within 3–5 days.