Cookie Dough: In a large bowl, beat butter, sugars, egg, and vanilla until creamy. Add flour 1 cup at a time, beat thoroughly after each addition. Cover and chill for 2 or more hours.
Filling: In a small saucepan, combine brown sugar, butter and corn syrup. Stir over medium heat until melted and just begins to boil. Remove from heat and stir in pecans. Set aside to cool, about 20-30 minutes.
Preheat oven to 350 degrees. Line 3 baking sheets with parchment paper.
Working in batches, shape cookie dough into 12 rounded 1-inch balls. Place 2-inches apart on prepared baking sheets. Press the centers down with your thumb. Use your fingers to smooth the edges if needed. Keep dough in the refrigerator between batches.
Bake for 6 minutes. Remove from oven so you can fill centers.
After baking, you may need to make your indentation again. Add a heaping 1/4 teaspoon of pecan pie filling to each cookie. Don't add too much or it will bubble over your cookie and look messy. They are still delicious, just not as pretty.
Bake for 5-7 more minutes or until golden brown. Cool on baking sheet.
Place cooled cookies in containers with tight-fitting lids, separating layers with waxed paper. Cookies can be stored in the freezer up to 3 months.