Make filling: In a small saucepan of boiling water blanch peach 1 minute and drain. Peel and pit peach and slice thin. In a small bowl toss peach slices with sugar, mint, and lemon juice.
Make shortcakes: Preheat oven to 425°F.
In a small bowl whisk together flour, sugar, baking powder, cinnamon, and a pinch salt. Add cream and stir with a fork until mixture just forms a dough. Turn dough out onto a lightly floured surface and with floured hands pat into a 6- by 3-inch rectangle. With a sharp knife trim edges and halve dough crosswise to form two 3-inch squares.
Arrange dough squares 2 inches apart on a lightly greased baking sheet and bake in middle of oven until golden, 12 to 15 minutes. (Squares will spread more than they will rise.) Transfer shortcakes to a rack and cool 10 minutes.
Make whipped cream: In a small bowl with an egg beater or electric mixer beat cream with sugar until it just holds soft peaks and beat in vanilla.
Split shortcakes with a serrated knife and put a bottom half on each of 2 plates. Top with peaches and any liquid, whipped cream, and shortcake tops.
