In a medium saucepan, combine the sugar and 1 cup of water. Heat over medium heat, stirring constantly until the sugar is completely dissolved to create a simple syrup. Remove from heat and let cool slightly.

While the syrup cools, chop the peeled and pitted peaches into roughly 1-inch chunks.

Place the chopped peaches, the remaining 3 cups of water, the cooled simple syrup, fresh lemon juice, and vanilla extract into a high-speed blender.

Blend on high speed for 2-3 minutes, or until the mixture is completely smooth and silky. If the mixture is too thick, add a splash more cold water until the desired consistency is reached.

For an extra smooth texture, strain the nectar through a fine-mesh sieve into a large pitcher, pressing gently on the solids to extract all the liquid. Discard any remaining pulp.

Chill the peach nectar in the refrigerator for at least 1 hour before serving. Serve over ice, garnished with a peach slice or mint sprig if desired.