Prepare Peach Syrup: In a medium saucepan, combine 1 cup of sugar and 1 cup of water over medium heat. Add sliced fresh peaches and gently mash them to release their juices. Stir until sugar dissolves, about 5 minutes.

Simmer: Once boiling, lower heat to a simmer and cover the pan. Let syrup simmer for 30 minutes, stirring occasionally.

Brew Tea: While syrup simmers, bring 6 cups of water to a boil. Steep 3 black tea bags for about 5 minutes, then remove tea bags and let cool.

Strain Syrup: Use a fine-mesh strainer to separate peach pieces from the syrup. Pour strained syrup into cooled tea, mixing well.

Chill: Transfer combined peach tea to a pitcher and refrigerate for at least 24 hours.

Serve: Once chilled, serve peach tea over ice in tall glasses. Garnish with a slice of fresh peach.