Preheat the oven to 350 degrees F. Grease a 9-inch cake pan, line it with a round of parchment paper cut to fit, and grease again.
Add the butter, applesauce, egg, and vanilla to a medium bowl. Beat with an electric mixer for about 1 minute.
Add the sugars and beat on medium for an additional minute.
Gently fold in the flour, oats, coconut, baking soda, salt, and chocolate chips.
Gently press mixture into the bottom of the prepared pan and press with a spoon to even out to the edges.
Bake for 24-26 minutes or until golden brown around the edges and just set in the center.
Let cool for at least 15 minutes before transferring to a cutting board, slicing into wedges, and serving.
Store any leftovers in an airtight container for up to 4 days.
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Notes
This cake can be made up to 1 day ahead, though it is best on the day that it's baked—it softens as it sits so you lose the slightly crunchy edges (but it's otherwise great!). If making it ahead, let it cool fully on a wire rack after Step 6. Store in an airtight container and store at room temperature.
Gluten-free: Use gluten free cup-for-cup flour and certified gluten free rolled oats.
If you don't happen to have applesauce, you can use mashed banana instead.
Chop the chocolate or use mini chips to evenly distributed it throughout the cake—so you get some in each bite.