Preheat oven to 425 degrees. In a food processor, combine flour, butter, baking powder, salt, and 1/3 cup sugar and process until mixture resembles coarse meal. Add milk and pulse just until moistened, 4 to 5 times.
Turn out dough onto a lightly floured surface. With floured hands, gently pat into a 4-by-8-inch rectangle. Cut dough into 8 squares and transfer to a baking sheet; sprinkle with 1 tablespoon sugar. Bake until golden, 25 to 30 minutes. Let biscuits cool on baking sheet.
In a large bowl, beat cream until soft peaks form. Add 2 tablespoons sugar and beat until soft peaks return. To serve, split biscuits with a serrated knife; sandwich with rhubarb compote and whipped cream.
For a delicate texture, don't add too much flour when forming the dough.