Prepare Peach Filling: If using fresh peaches, blanch, peel, pit, and dice. For canned, drain peaches. Mix sugar, cornstarch, cinnamon, nutmeg, and salt. Cook peaches with mixture, lemon juice, vanilla, and butter until thickened. Cool completely.
Make Cobbler Topping: Preheat oven to 375°F. Mix flour, sugars, baking powder, and salt. Cut in cold butter until crumbly. Add milk and vanilla, stir into a dough. Spread on baking sheet and bake until golden. Cool and crumble.
Prepare Cream Cheese Whipped Cream: Beat softened cream cheese with powdered sugar and vanilla until smooth. Whip cold heavy cream until stiff peaks. Fold whipped cream into cream cheese mixture. Chill until assembly.
Assemble Parfaits: Layer cobbler crumble, peach filling, and whipped cream in glasses. Repeat layers and top with a swirl of whipped cream. Chill for 30 minutes.
Garnish and Serve: Decorate with mint and peach slices. Serve immediately or refrigerate for up to 2 days.
Notes
For best results, chill components before assembly and serve promptly for optimal texture.