Preheat oven to 325F degrees. Spray muffin tins with nonstick spray or use cupcake liners. (Muffins may stick to liners so spray them as well if you use liners.)
In a large bowl, add flour, baking soda, and salt.
In a separate bowl, mix the honey and brown sugar together. It will be thick. Add the apple sauce, yogurt, and beaten egg.
Pour the wet ingredients into the dry ingredients. Add milk. Fold together carefully. It will be thick. Add more Greek yogurt 1 T at a time if you feel they are too thick. Gently fold in the blackberries. Do not overmix or muffins wil be tough.
Divide the batter between 12 muffin tins. Fill 3/4 full. You may have more than 12 muffins depending on the size of your tins. Just fill another tin if you do. Bake for 18 to 20 minutes until lightly browned on the edges. When done, the center should spring back after being touched.