Prepare the simple syrup by combining the sugar and water in a medium saucepan. Heat over medium-high heat, stirring until the sugar dissolves. Bring to a boil. Boil 1 minutes, then remove from heat to cool. (You won't use all of it here, but you can refrigerate and use extra for other cold drinks like iced tea or coffee).
Make the peach puree by adding diced peaches and 1/4 cup cooled simple syrup to a blender (or food processor). Blend until smooth. Taste and add additional simply syrup if needed. Puree should be pleasantly sweet. Refrigerate until well chilled.
To make the drink, add a bit of the chilled peach puree to the bottom of a glass (about 1/4-1/3). Top up with Prosecco. Give a stir, add 3 frozen raspberries and add a fresh mint sprig. Enjoy!