For the marinated peaches: Mix together the granulated sugar, orange liqueur, basil and orange zest in a bowl. Add the peaches and toss to coat. Cover and refrigerate for at least 1 hour.
For the sweet biscuits: Preheat the oven to 375 degrees F.
In a bowl, mix together the flour, granulated sugar, baking powder and salt. Cut in the butter using a pastry cutter until it is incorporated. Mix the buttermilk and vanilla together in a small pitcher. Slowly add the buttermilk mixture into the flour mixture, stirring the contents of the bowl as you do so, until just combined.
Form 6 biscuits and place them into a cast-iron skillet. Sprinkle the tops generously with coarse sugar. Bake until golden brown, 24 to 26 minutes. Allow to cool for 10 minutes before serving.
For the whipped cream: Using an electric mixer, whisk together the heavy cream and granulated sugar until soft peaks form.
To serve, halve the biscuits, then place the bottom halves on serving plates. Top with the whipped cream and marinated peaches. Rest the biscuit tops on the side so the filling is visible. Garnish with torn basil.