Preheat oven to 350°F (176° C) and line a baking sheet with parchment paper or a silicone baking mat.
Make the Pecan Pie Filling: Combine the cold water and cornstarch in a small bowl, stirring until smooth and silky, and set aside. In a saucepan, melt the butter over low heat. When it starts to bubble, stir in the chopped pecans, brown sugar, corn syrup, and vanilla extract. Cook gently for about 1 to 2 minutes, stirring continuously.When the mixture begins to bubble again, pour in the cornstarch slurry and stir to combine. Continue cooking for 2 to 3 more minutes, or until the mixture thickens and looks shiny. Remove from heat and let it cool slightly while you prepare the cookie dough. Mix wet ingredients: In a large mixing bowl, use an electric mixer to cream the butter and sugar until light and fluffy, about 2-3 minutes. Add the egg, vanilla extract and sourdough starter discard and beat until combined.
Add dry ingredients: Whisk the all-purpose flour, salt, and baking powder in a medium bowl. Add the dry ingredients to the wet ingredients, and use a spatula or wooden spoon to incorporate them. When the mixture becomes too difficult to mix with a wooden spoon, switch to using your hands. Press the dough together until it becomes a stiff dough.
Shape the cookies: Use a cookie scoop to portion about 2 tablespoons of dough and roll it into a smooth ball. Place the dough ball on the prepared baking sheet, then press the center with your thumb or the back of the cookie scoop to create a small well. Spoon about ½ teaspoon of pie filling into the center and sprinkle chopped pecans on top. Repeat the process with the remaining dough.
Bake: Bake the cookies for 13-15 minutes. Remove them from the oven and allow them to cool on the baking sheet for 10 minutes before transferring to a cooling rack.