Preheat oven to 375° F. Line a large baking sheet with parchment paper.
Beat the butter until smooth, then slowly add the confectioners' sugar, vanilla extract and flour. Beat on low speed until well-blended. Stir in the pecans and mix well.
Shape the dough into 1-inch-diameter balls and place them on the baking sheet about 1 1/2 inches apart. Use your thumb to press down the center of each ball, to make a depression that will later be filled with Praline Sauce. Bake for 11 to 13 minutes, or until the edges of the cookies are very light brown. Do not over-bake.
Remove from oven and place the baking sheet on a wire rack. Let the cookies cool on the parchment paper on the baking sheet. While the cookies are cooling, make the Praline Sauce. Working quickly, spoon a little of the Praline Sauce into the depression in each cookie.
Let the cookies set for at least one hour before storing or eating.
Combine 1/4 cup butter, 1/2 cup brown sugar, 1/4 cup evaporated milk and a pinch of salt in a saucepan. Cook over medium heat, stirring constantly, until the mixture starts bubbling. Reduce the heat to low and cook for 5 minutes longer.
Remove the pan from the heat and stir in 1 cup granulated sugar and 1/2 teaspoon vanilla extract.
Makes: 36 cookies