Mise en place. Preheat oven to 350˚F and grease a 9x13-inch baking dish. Then, measure and prep all of your ingredients before starting.
Mix the dry ingredients. In a medium mixing bowl, whisk the flour, baking powder and salt together until combined. Set aside.
Beat the wet ingredients. In a large bowl with an electric mixer, beat the peanut butter with sugar until light and fluffy. Add oil and mix until combined. Next, beat in the eggs, one at a time, until each in incorporated. Then, mix in vanilla.
Combine wet and dry. Alternate between adding the flour mixture and dairy-free milk to the mixer, making sure each addition is incorporated before adding the next.
Make the jam swirl. Heat the raspberry jam in the microwave for about 1 minute. Then, mash or chop raspberries and stir them into the warmed jam.
Assemble the cake. Pour the batter into the cake pan and dollop the jam mixture on top. Use a toothpick or chopstick to swirl the jam into the batter.
Bake the cake. Place the cake into the oven for 35 - 40 minutes, or until the top of the cake has set and an inserted toothpick comes out clean.