Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the flour, sugar, baking powder, and salt. Stir until well mixed.
Add the milk, melted butter, peanut butter, and vanilla extract to the dry ingredients. Mix until just combined; do not overmix.
Pour the batter into a greased 9x13-inch baking dish.
Spoon the jelly or jam evenly over the top of the batter.
Using a knife or a skewer, gently swirl the jelly into the batter to create a marbled effect.
Bake in the preheated oven for 30-35 minutes, or until the top is golden brown and a toothpick inserted in the center comes out clean.
Allow the cobbler to cool for about 10 minutes before serving.