Preheat oven to 350 degree. Grease a 9-inch square cake pan then line partially with parchment paper (This just makes it easier to remove from the pan but you can skip that step if you’d prefer.)
In a large bowl, whisk together applesauce, egg, oil, maple syrup, milk, and vanilla.
In a second bowl, mix remaining ingredients besides the strawberries and jam, if using. (You can also just add the dry ingredients to the wet ingredients one-by-one if you prefer not getting another bowl dirty. However, I think the dry ingredients incorporate better if they are mixed together first.)
Add the bowl of dry ingredients to the wet ingredients and mix until almost all the flour is combined. Stir in about 3/4 of the diced strawberries and mix just until combined to avoid overmixing. Pour the batter into your prepared pan and spread it evenly into the pan. Scatter the remaining strawberries over the top, then sprinkle on a pinch of extra oats. (The oats are just for a garnish so totally optional.)
Bake until golden brown around the edges and cooked through, about 27 to 35 minutes (depending on what type of pan you are using). Allow to cool completely then cut into squares. Store in an airtight container on the counter for 2 days or in the fridge for 5 days.