Prep. Preheat the oven to 350°F (175°C). Grease a 9-inch square baking dish or any similar-sized baking dish.
Make the topping. In a medium bowl, use an electric mixer to beat the butter, sugar, and egg yolk until light and creamy. Then, add vanilla extract, followed by flour, baking powder, and salt. Mix on low speed until the batter is smooth and well combined. The batter will be thick, resembling wet cookie dough.
Assemble. In a separate bowl, mix the lemon zest and juice into the lemon pie filling. Then, pour the lemon pie filling evenly into the prepared baking dish. Carefully spoon the cookie dough topping over the lemon pie filling in dollops, then gently spread it across without mixing it into the filling.
Bake. Place the baking dish in the preheated oven and bake for 30-35 minutes, or until the topping is golden brown and set. For an extra touch of sweetness, sprinkle coarse sugar on top during the last 5 minutes of baking.
Serve. Allow the cobbler to cool for a few minutes before serving.Dust with powdered sugar if desired and serve warm with vanilla ice cream or whipped cream.