Preheat the oven to 375 degrees. If you’re not using paper liners, lightly grease a muffin tin.
Combine the oats, milk and vinegar (your “buttermilk”—the vinegar will react with the baking powder later) in a mixing bowl. Let the oats soak for at least 5 and up to 30 minutes. Add the oil, cashew butter, honey, and vanilla. Stir by hand until just combined.
Add the flour(s), baking powder, baking soda, and salt. Stir until evenly incorporated.
Before adding the berries, scoop a tablespoon of batter into each muffin tin. This will prevent the blueberries from sinking to the bottom of the muffins. Gently fold the blackberries into the remaining batter and divide evenly between the muffin tins.
For the streusel, combine the flour, oats and brown sugar together. Sprinkle a small spoonful of crumbs over each muffin before baking.
Bake muffins for 13-15 minutes, or until golden brown.