Preheat the oven to 375°F/190°C. Grease an 8 x 8 in/20 x 20 cm baking dish.
In a bowl, combine the rolled oats, whole wheat flour, nuts, raisins, baking powder, cinnamon, and salt.
In a spouted measuring cup combine the milk, water, eggs, applesauce, and vanilla extract. Whisk together.
Pour the wet ingredients into the bowl with the oat mixture. Stir to combine.
Scrape the batter into the prepared baking dish. Dollop the jam into the batter in a 3x3 grid.
Bake in a preheated oven the edges begin to pull away from the pan and the top is golden brown, about 30 to 35 minutes.
Serve warm or chilled.