Juice orange (should get 1/4 cup) and juice lemons (should get 1/2 cup). Reserve juices then add both spent orange halves and one spent lemon half to a small saucepan. Crack cinnamon sticks in half and add to saucepan. Add ginger, tea bags, peppercorns, cloves, and water to saucepan.
Bring to a boil over high heat then reduce to medium and simmer 2 minutes. Remove tea bags, stir in honey (start with 1/4 cup and add more to taste. I usually use 1/3 cup.) and let mixture steep 20 minutes.
Strain mixture through a fine mesh sieve; discard solids.
Add spiced honey mixture to a large pitcher. Add orange, lemon juice, and rye whiskey. Add 1 cup ice and stir until completely melted and toddy is cold.
Serve toddy over ice in rocks glasses; garnish with an orange twist (and candied ginger if you’re feeling fancy).
To make this warm—skip adding the ice and instead add 1/2 cup hot water. Serve in mugs and garnish with an orange slice. Top each toddy with additional hot water to taste.