In a microwave safe dish, heat buttermilk for 30 seconds. You want it to be warm, but not hot.
Once buttermilk is warm, add oil and stir to combine.
In a separate bowl combine flour, sugar, and salt.
In a large bowl, mix together buttermilk and oil and yeast with a spoon. Allow to rest for 5 minutes. Add 3 cups of flour and egg to the bowl and knead manually or using dough hook until combined. If dough is still sticky after all the flour has been kneaded in, add remaining 1/2 cup of flour and knead until the dough it soft and no longer sticking to the sides.
On a lightly floured surface, roll dough out into a large rectangle approximately 1/2inch thick.
Spread softened butter evenly over the surface of the dough.
Combine blackberries and cornstarch, set aside.
Sprinkle cinnamon and sugar over dough.
Sprinkle blackberries over cinnamon and sugar.
Beginning with the horizontal side closest to you, tightly roll dough to opposite side, pinching the seam together at the end.
Cut rolls into 12 even pieces and place in a greased 9x13 pan.
Cover pan with a warm damp cloth and allow rise for about 25 minutes in a dark warm place.
Once rolls have risen, bake at 400 degrees for 15 minutes, or until slightly browned.
Whisk cream cheese, jam, milk, and powdered sugar until smooth.
Pour over warm rolls.
Makes 12 cinnamon rolls.