Step 1: In a large bowl, combine the peeled, pitted, and sliced peaches with the granulated sugar, light brown sugar, cornstarch (or tapioca starch), cinnamon, optional ginger, and optional nutmeg. Toss gently until the peaches are evenly coated. Let stand for 10-15 minutes to allow the peaches to release some of their juices.
Step 2: Transfer the peach mixture to a large saucepan or Dutch oven. Add the lemon juice. Cook over medium heat, stirring occasionally, until the mixture begins to thicken and bubble gently, about 8-10 minutes. The peaches should be tender but still hold their shape.
Step 3: Once thickened, remove the saucepan from the heat. Stir in the unsalted butter until it is completely melted and incorporated, adding richness and a beautiful sheen to the filling.
Step 4: Taste the filling and adjust sweetness or spices if necessary. If using immediately for a pie, allow it to cool slightly before pouring into your pie crust. If preparing in advance, transfer to an airtight container and refrigerate for up to 5 days, or freeze for longer storage.
Step 5: To use in a pie, simply pour the cooled filling into your unbaked pie crust, top with a second crust or lattice, and bake according to your pie recipe's instructions until golden brown and bubbly.