Gather five or six not-too-ripe peaches. Cut them in half, remove the pits, then cut each half into 4 pieces. Arrange them in a baking dish, sprinkle them with about a tablespoon of flour, toss to coat. Squeeze lemon juice on top, drizzle on a few spoonfuls of honey, and set aside.
To make the topping, put 1/2 cup of heavy cream and five tablespoons of sour cream in a large bowl and stir well. In a separate bowl combine 1 1/4 cups of flour, 1/4 cup of sugar, one teaspoon of baking powder, 1/4 teaspoon of baking soda, and a pinch of salt. Add four tablespoons of unsalted butter to the flour mixture, and rub together with your fingers until crumbs form. Add the flour mixture to the cream mixture using a fork to stir. This topping will be very sticky. Drop spoonfuls on top of the peaches, leaving gaps to expose the fruit. Sprinkle a few spoonfuls of sugar over the top. Bake for about 30 minutes, until golden, at 375F.
Serve slightly cooled, still warm, with vanilla ice cream on top.
