In a medium saucepan, combine pecans and 1/3 cup sugar, and heat over low heat until sugar is completely melted, stirring occasionally with a metal spoon.

Pour pecan mixture onto wax paper and let cool completely. Once praline has cooled, finely chop up the praline using either a knife, food processor, or a plastic bag and rolling pin until there are only a few larger pieces of pecan visible. Set aside.

Beat together butter and sugar until light and fluffy. Add salt and vanilla extract, and beat to combine.

Add flour, about half a cup at a time, until flour is well incorporated.

Fold chopped candied pecans into the dough.

Divide the dough in half, and form each half into a long log about 1 1/2 inch in diameter. Wrap each log in plastic wrap, and chill for one hour.

Cut logs into 1/4 inch thick slices. Place the cookie slices onto the prepared baking sheet, leaving a bit of space between the cookies.

Bake for 10-15 minutes, or until cookies are lightly golden.

Let cookies cool on sheet for 5 minutes, then transfer them to cooling rack and let them finish cooling.