Preheat oven to 350°F and grease a 13” x 9” baking pan with nonstick cooking spray. Line baking pan with parchment paper sling, pushing parchment into corners and up sides of pan. In a large bowl, sift flour, baking powder, baking soda and salt together until combined.
In a separate large bowl, whisk sweetener, oil, ½ cup peanut butter, eggs and vanilla together until smooth. Add flour mixture and milk in 2 alternating batches, beating well between each addition, until just combined. Pour batter into prepared pan.
Dollop remaining peanut butter and jam on top of batter and gently swirl together with a butter knife or rubber spatula.
Bake until a toothpick inserted into the center comes out clean, about 30-40 minutes. Let cool on wire rack for 1 hour before slicing and serving.
Note
Substitute your favorite sugar-free jam for the blackberry jam!