Place the oats, baking powder, cinnamon, salt, sugar, and ground flax seeds into the bowl of a food processor. Process for about 30 seconds or until the oats resemble a coarse flour.
Stir all ingredients together in a bowl. (Or, add all ingredients to the food processor, adding the chopped apples last, and pulse to combine if you don't want to dirty another bowl.)
Pour into the prepared baking pan and smooth the top with a spatula until even.
Bake for 32-34 minutes or until a cake tester inserted into the center comes out clean and the edges are lightly golden brown.
Place pan onto a wire rack and let cool completely before cutting.
Store in an airtight container in the fridge for up to 5 days or at room temperature for 3 days. We prefer it chilled, but it works either way.
Yogurt Icing: Stir together 1/4 cup plain whole milk Greek or regular yogurt with 2 tablespoons honey or maple syrup. Spoon into a plastic storage bag. Seal, then cut off one bottom corner. Drizzle over the cooled bread.
Egg-Free: Omit the eggs and increase the milk to 3/4 cup. Soak 3 tablespoons chia seeds in the milk before adding to the batter. Decrease baking time to 30 minutes.
Gluten-Free: Use certified gluten-free oats.
Dairy-Free: Use coconut oil instead of butter and nondairy milk.
Use maple syrup instead of sugar if you prefer.
Use smooth applesauce that's unsweetened.
Use whichever apples you prefer, though I like Granny Smith, Cortland, or Pink Lady. Dice them into small pieces.
Serve this bread chilled straight out of the fridge or slightly warmed.