In a medium bowl combine boysenberries and cornstarch. Toss to coat.
Add the remaining filling ingredients and gently stir together. Pour into an 8x8 baking dish or four 4" custard dishes.
In another bowl combine oats, flour, brown sugar, and salt. Cut the butter in small cubes and add. With your fingers, press the butter into the oat/flour mixture until it resembles small pea-size pieces. Top berries with oat crisp and firmly pat down.
Bake for 25-30 minutes, until the tops are browned and the filling begins bubbling up.