In a medium-sized bowl, combine the flour, cornstarch, powdered sugar, baking soda, and salt. Stir well to ensure everything is evenly distributed. Set aside.
In a separate large mixing bowl, add the oil, granulated sweetener, applesauce, and vanilla extract. Using a hand mixer on low speed, beat the ingredients together for 1-2 minutes until well combined and the mixture is slightly creamy.
Gradually stir in the dry flour mixture until fully incorporated. The dough should be thick yet soft. If it seems too stiff, add 1-2 tablespoons of non-dairy milk to loosen it slightly.
Cover the dough and refrigerate for at least 30 minutes. This will help prevent excessive spreading during baking.
Filling
In a small bowl or measuring cup, mix 2 tablespoons of coconut milk with the cornstarch until smooth. Set this slurry aside.
In a heavy-bottomed pan over medium heat, combine the coconut oil, 4 tablespoons of coconut milk, brown sweetener, and maple syrup. Stir frequently until a translucent syrup forms and begins to simmer gently.
Reduce the heat to medium-low and stir in the chopped pecans. Let the mixture boil lightly for 3 minutes, stirring frequently until it starts to thicken slightly.
Add the prepared cornstarch slurry, vanilla extract, and ground cinnamon to the syrup. Stir continuously for 2-3 minutes until the filling becomes very thick and takes a couple of seconds for any cleared area in the pan to fill back in.
Remove the filling from heat and allow it to cool completely before using.
Assembly and Baking
Preheat the oven to 350°F and line your baking sheets with parchment paper.
Scoop slightly heaping 2-tablespoon portions of dough, rolling them into smooth balls. Place the dough balls onto the lined baking sheets, spacing them 2-3 inches apart.
Use your fingers, the back of a round spoon, or a small bowl to press down each dough ball and create a deep well in the center. Smooth out any cracks around the edges to keep the shape intact.
Spoon about 1 tablespoon of the cooled filling into the well of each cookie.
Bake the cookies in the preheated oven for 9-11 minutes, or until the edges are firm and slightly golden.