In a large skillet over medium heat, combine fresh or frozen blackberries, granulated sugar, water, lemon juice, ground cinnamon, and vanilla extract. Stir gently until the mixture starts to simmer and the sugar dissolves, which should take about 5 minutes.

In a medium bowl, whisk together the all-purpose flour, baking powder, granulated sugar, salt, and remaining ground cinnamon.

Cut cold unsalted butter into the dry ingredients until the mixture looks like coarse crumbs.

Mix buttermilk and a splash of vanilla extract in a separate bowl, then gradually pour this mixture over the dry ingredients, stirring gently until just moistened.

Drop the dough by tablespoonfuls into the simmering blackberry sauce, cover the skillet with a lid, and reduce heat to low. Allow the dumplings to steam for 12-14 minutes.

Check for doneness using a digital thermometer; they should reach 195°F (91°C).

Let the dumplings rest for about 5 minutes before serving them warm with a scoop of vanilla ice cream or whipped cream.