Preheat oven to 350°F. Line a baking sheet with parchment and set aside.
Cream together the butter and sugars until smooth. Beat in the eggs and vanilla.
Combine the 1 ½ cup of flour, cornstarch, baking soda and salt in a separate bowl and add to the creamed mixture, mixing just enough to combine. Gently mix in the oats and white chocolate chips. Dough will be stiff.
Place the remaining 2 TBSP flour in a small bowl and gently coat HALF of the blackberry pieces. (Blackberries should be cut into dime sized pieces. I just cut most of mine in half, but larger berries might need more cutting.) Gently fold the blackberries into the cookie dough. Some will be crushed, but do your best to not smash them.
Use a cookie scoop to drop cookies onto a greased cookie sheet. Top with remaining blackberry pieces, as well as a few more white chocolate chips. Bake for about 9-10 minutes at 350°F.
Cool on the baking sheet for about 5-7 minutes before transferring to a wire rack to cool completely. Enjoy!
Notes
Store leftovers in an airtight container on the countertop.