Preheat oven to 375°F and line a 12-cup muffin tin with muffin liners.
In a large bowl, whisk together 1/3 cup Greek yogurt, 2/3 cup cane sugar, 1/3 cup avocado oil, 2 tsp lemon zest, 2 tsp vanilla extract, and 3 eggs until smooth. In a separate bowl, mix 1 cup oat flour, 1 1/3 cups gluten-free flour, 1 1/2 tsp baking powder, 1/4 tsp baking soda, and 1/2 tsp salt. Gradually add the flour mixture to the wet mixture, stirring gently with a wooden spoon. Fold in 1 cup blackberries, being careful not to overmix.
In a small bowl, combine 1/4 cup old-fashioned oats, 2 tbsp butter, 2 tbsp cane sugar, 1/4 tsp salt, and 1/4 tsp vanilla extract. Mix with a fork until the mixture forms small crumbles.
Divide the muffin batter evenly into the prepared muffin cups, filling each about 3/4 full. Sprinkle the oat crumble topping evenly over each muffin. Optional: Add more chopped blackberries.
Bake in the preheated oven for 25-29 minutes or until a toothpick inserted into the center comes out golden brown and clean. Let muffins cool in the 12-cup muffin pan for 5 minutes before transferring to a wire rack.