To make the rosemary and mint simple syrup: Combine the rosemary, mint, sugar, and 2 cups water in a pot and simmer over low heat until the sugar dissolves and the herbs are steeped, about 5 minutes. Turn off the heat and let the mixture cool to room temperature. Strain, place in a bottle, and store in your fridge.
To make the tea: Bring 1 gallon water to a simmer in a large pot. Put the tea leaves into a large tea bag or tea ball or in cheesecloth. Tie or secure. Turn off the heat, add the tea to the water and steep until flavorful, about 5 minutes.
Remove the tea leaves. Let the tea cool. Transfer the tea to a drink dispenser and add the mint and rosemary sprigs. Add 1 1/2 cups of the simple syrup and stir to combine; taste and add more syrup if you want the tea sweeter. Serve the tea over ice.