In a medium saucepan over medium heat, cook the blackberries, sugar, and water for 15 minutes. Mash the blackberries as they cook to help them break down. You know the mixture is ready when it resembles the texture of jam and pulls away from the bottom of the pan. Remove from heat, stir in vanilla extract, and allow to cool slightly.
Preheat oven to 350°F and line an 8″x8″ glass pan with parchment paper. Set aside.
In a standing mixer fitted with paddle attachment, beat the butter and sugars for 1-2 minutes, until light and fluffy. Beat in the egg and vanilla extract for another minute.
In a separate bowl, combine flour, baking soda, salt, and nutmeg. Stir flour mixture, along with oats, into the wet ingredients.
Place half of batter into prepared pan, spreading to the edges. Dollop in blackberry jam. Break remaining oatmeal batter into pieces and place over jam. Bake for 30 mins, or until a knife inserted in the center of the bars comes out clean. Allow to cool slightly before serving!