Step 1: Prepare the peaches. Bring a large pot of water to a boil. Score a small ‘X’ on the bottom of each peach. Carefully immerse peaches into boiling water for 30-60 seconds, or until skins start to wrinkle at the ‘X’.
Step 2: Immediately transfer peaches to an ice bath (bowl of ice water) to stop the cooking. Once cooled, peel off the skins, which should slip off easily.
Step 3: Slice each peeled peach in half, remove the pit, and then cut into roughly 1/2 to 3/4-inch slices. You should have about 6 cups of sliced peaches.
Step 4: In a large, heavy-bottomed pot or Dutch oven, combine the sliced peaches, granulated sugar, brown sugar, and lemon juice. Stir gently to coat the peaches. Let stand for 15-20 minutes to allow the peaches to release their juices.
Step 5: While peaches are macerating, prepare the cornstarch slurry: in a small bowl, whisk together cornstarch and 1/4 cup cold water until smooth. Set aside.
Step 6: Place the pot of peaches over medium heat. Bring to a gentle simmer, stirring occasionally. Cook for 5-7 minutes, or until peaches are tender but still hold their shape.
Step 7: Slowly pour the cornstarch slurry into the simmering peach mixture, stirring constantly. Continue to stir and cook for another 2-3 minutes, or until the filling thickens to your desired consistency. It should be thick enough to coat the back of a spoon.
Step 8: Remove the pot from the heat. Stir in the ground cinnamon and nutmeg (if using). Taste and adjust seasonings as needed.
Step 9: Allow the peach pie filling to cool completely before using or storing. The filling will thicken further as it cools. Store in an airtight container in the refrigerator for up to 5-7 days, or freeze for up to 6 months.