Heat your Blackstone griddle to medium heat or around 350 degrees F (175°C). Make sure the griddle is evenly heated before proceeding.
Combine sliced apples, granulated sugar, cornstarch, brown sugar, ground cinnamon, lemon juice, and diced unsalted butter in a large bowl. Toss the mixture until the apples are evenly coated.
Add 2 tablespoons of unsalted butter to a large skillet over medium heat; add the apple mixture and saute for a couple of minutes until softened.
While the apples are cooking, prepare the cobbler topping. Combine oats, all-purpose flour, brown sugar, and ground cinnamon in a separate bowl. Cut in cold, diced, unsalted butter using a pastry cutter or your fingertips until the mixture resembles coarse crumbs.
Add 1/2 of the apple filling to the bottom of a piece of foil. Then add about 1/2 of the cobbler topping. Wrap tightly, and place the foil packets onto the Blackstone Griddle.
Cook for approximately 20-25 minutes until the cobbler topping turns golden brown and is cooked through.
Carefully remove the apple cobbler from the griddle. Allow it to cool slightly before serving. You can enjoy it warm on its own or pair it with a scoop of vanilla ice cream, a dollop of whipped cream, or a drizzle of caramel sauce for added indulgence.