In a mixing bowl, whisk together flour, sugar, baking powder, and salt until evenly combined. Add milk and vanilla extract, then mix until a smooth batter forms. Make sure there are no lumps for a soft and even bake.
Pour the melted butter into your baking dish, spreading it evenly across the bottom. This creates a rich base and helps form a golden crust. Do not stir the butter with the batter—it works as a separate layer.
Gently pour the batter over the melted butter without mixing. Spoon dollops of peanut butter and strawberry jam evenly across the top. As it bakes, these layers will sink and swirl naturally.
Place the dish in a preheated oven at 350°F (175°C) and bake for 35–40 minutes. The top should be golden brown, and the edges slightly crisp. The center will remain soft and gooey.
Allow the cobbler to cool for about 10 minutes before serving. This helps the flavors settle and makes scooping easier. Serve warm for the best experience.