In a large pitcher, combine the apple cider, fresh lemon juice, fresh orange juice, orange slices, fresh thyme sprigs, cinnamon sticks, diced apples, and bourbon if you're using it. Stir everything together to ensure all the flavors start to blend. I like to use a wooden spoon to gently bruise the thyme sprigs and release more of their aroma into the drink.
Let the mixture sit for about 30 minutes if you have time; this allows all the flavors from the fruits, thyme, and cinnamon sticks to fully infuse into the liquid. If you're short on time, you can serve it immediately, but the flavor will be more vibrant after resting.
When you're ready to serve, pour the bottle of Prosecco into the infused mixture and stir gently to combine. Be careful not to over-stir so you don't lose the bubbles. Pour the sangria into individual glasses and garnish each with thyme sprigs, cinnamon sticks, and some of the fruit from the pitcher. For a festive touch, I sometimes rim the glasses with a little sugar and cinnamon.