Bring 4 cups of water to a rolling boil in a saucepan.
Remove from heat and add black tea bags or loose tea.
Steep for exactly 5 minutes, then remove the tea bags.
Bruise rosemary sprigs by rolling between palms or lightly pressing with a knife.
Add bruised rosemary to the hot tea and let steep for 10–15 minutes.
Zest 1 orange (about 2 tbsp), avoiding the bitter white pith.
Juice both oranges and set aside.
Remove rosemary from tea, then stir in honey or maple syrup while still warm.
Add orange zest and juice to the tea.
Add remaining 2 cups of cold water.
Refrigerate the tea for at least 2 hours to chill and infuse.
To serve, fill glasses with ice, pour chilled tea, and garnish with fresh orange slices and rosemary sprigs.