Preheat oven to 350 degrees.
Prep a 9X13″ baking dish with baking spray. Add sliced apples, brown sugar, and 1 teaspoon cinnamon in a bowl. Toss to coat.
Melt 1/4 cup of butter in a large skillet over medium-low heat. Add the apple mixture.
On medium-low heat cook the apples for 5-8 minutes stirring often. (Until the apples just become translucent.) Set aside to cool.
Using a paddle attachment cream 3/4 cup butter and 3/4 cup sugar in the bowl of a stand mixer. Add the egg and vanilla. Beating as you add them. Mix in baking soda, cream of tartar, and salt. Slowly mix in the flour.
Pour the cooked apples into the prepared 9×13” baking dish. Spoon tablespoons of the dough mixture evenly over the top in a single layer.
In a small bowl mix the 1/3 cup sugar and 2 teaspoons cinnamon. Sprinkle evenly over cookie dough.
Bake at 350 degrees for about 24-26 minutes. (Or until the cookie dough starts to brown.) Cool slightly before serving.
Serve the snickerdoodle apple cobbler warm with ice cream or whipped cream.