In a mixing bowl, mix together the raspberries, 1 tablespoon of white sugar, 1 tablespoon of brown sugar, and 1 tablespoon of all-purpose flour.
Melt the butter in the microwave.
In a separate mixing bowl, mix together 1 cup of all-purpose flour, the heavy cream, 1 cup of white sugar, the melted butter, baking powder, and salt until well incorporated.
Pour the batter into an oven-safe dish and place the raspberries evenly on top. Top the cobbler with 2 tablespoons of white sugar.
Bake the cobbler for 40 minutes.
Remove the cobbler from the oven and let it cool for 10 minutes.
Slice the cobbler and enjoy with either whipped cream or ice cream.