Preheat an oven to 350 degrees F (175 degrees C). Grease a tube pan.
Flatten each dinner roll into a circle, then place about 1/2 teaspoonful blackberry jam onto the center of the dough.
Roll the filled dough into a ball, then transfer the dough into the prepared pan.
Bake in the preheated oven until golden brown, about 30 minutes.
Combine the corn syrup, butter, and vanilla extract in a small bowl.
Pour over the baked rolls, and allow syrup to be absorbed before removing from the pan. To remove from the pan, run a paring knife between the bread and the edge of the pan. Hold the pan on its side and gently tap the sides of the pan against the counter to loosen it. Cover the pan with a plate or cooling rack, and invert it to tip the bread out of the pan and onto the plate.
