Wash, core, and chop the apples into chunks, leaving the skins on for added flavor and nutrients.
In a large pot, bring the water to a boil over medium heat.
Once the water reaches a boil, add the chopped apples to the pot.
Reduce the heat to low and let the apples simmer in the water for about 30 minutes, or until they are soft and tender.
Stir in the granulated sugar or honey until completely dissolved, adjusting the sweetness to taste.
Remove the pot from heat and allow the apple mixture to cool to room temperature.
Once the mixture has cooled, sprinkle the active dry yeast over the surface and stir gently to combine.
Cover the pot with a clean cloth or lid and let the mixture ferment at room temperature for 2-3 days, allowing the natural fermentation process to occur.
After fermentation, strain the Kvas through a fine-mesh sieve to remove any solids, if desired.
Transfer the strained Kvas into clean, airtight bottles or jars and refrigerate for several hours before serving.
Serve the chilled Russian Apple Kvas in glasses or mugs, optionally garnished with a slice of apple or a sprinkle of cinnamon.