Bring a large pot of water to a boil, then carefully lower peaches into the hot water for 1-2 minutes to loosen the skins. Remove with a slotted spoon and let cool slightly, then peel away the skin using a paring knife. Halve each peach, remove the pit, and slice into 1/2-inch thick wedges. I find scoring the peach skin before blanching makes peeling much faster and easier—just make a shallow X on the bottom before the water bath.

Place the sliced peaches in a medium saucepan and add just enough water to barely cover them (approximately 1 inch). Bring to a simmer over medium heat and cook for 15-20 minutes until the peaches are very soft and easily break apart with a spoon. The peaches will release their juices and create a flavorful cooking liquid that becomes part of your sauce.

Transfer the cooked peaches and their cooking liquid to a blender and blend until completely smooth. For a silkier texture, I like to strain the blended sauce through a fine-mesh sieve to catch any small peach fibers, though this is optional depending on your texture preference. Pour the blended sauce back into the saucepan.

Add the granulated sugar, fresh lemon juice, vanilla extract, and salt to the blended peach sauce. Stir well to combine all ingredients, then bring the sauce to a gentle simmer over medium heat. Cook for 8-10 minutes, stirring occasionally, until the sugar has completely dissolved and the sauce has thickened slightly. Taste and adjust sweetness or acidity as needed by adding a touch more sugar or lemon juice.