Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or butter.
In a large mixing bowl, whisk together the flour, baking powder, salt, and sugar until well combined.
In another bowl, mix the melted butter, milk, peanut butter, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Do not overmix; a few lumps are okay.
Pour the batter into the prepared baking dish, spreading it evenly.
Drop spoonfuls of jelly over the batter, then use a knife or skewer to swirl the jelly into the batter gently.
If desired, sprinkle chopped peanuts over the top for added crunch.
Bake in the preheated oven for 30-35 minutes, or until the cobbler is golden brown and a toothpick inserted into the center comes out clean.
Let the cobbler cool for about 10 minutes before serving.