Place the tea bags (or loose leaves in a filter) into a large pitcher. Add the cold water, cover, and refrigerate for 6–12 hours, depending on desired strength. Do not stir or agitate during brewing.
Remove the tea bags or strain out the leaves. Stir in 2 tablespoons of honey until fully dissolved. Taste and add up to 1 additional tablespoon only if needed.
Add the strip of lemon peel to the cold-brewed tea. Let infuse in the refrigerator for 10–15 minutes only, just until a gentle citrus aroma develops. Remove the peel promptly.
Fill glasses with ice, pour over the cold brew iced tea, and garnish with a lemon slice or twist if desired.