Southern blackberry cobbler (aka blackberry doobie)

Ingredients

For the blackberry broth:

• 2 pints of fresh blackberries, about 2 ½ - 3 cups (I've never used frozen, but I imagine you could.)
• Water to cover
• ½ cup of sugar (or more, depending on the sweetness of the blackberries)
• 2 tablespoons fresh lemon juice

For the dumplings:

• 1 cup all purpose flour
• 1 teaspoon baking soda
• ½ teaspoon salt
• 2 tablespoons sugar
• 2 tablespoons cold butter, cut into small cubes
• ½ cup buttermilk
• 2 tablespoons brown sugar
• A pint of good vanilla ice cream