1. Preheat oven to 350°. Bake pecans in a single layer in a shallow pan 6 to 8 minutes or until toasted and fragrant, stirring halfway through.
2. Beat butter and sugar at medium speed with an electric mixer until fluffy. Gradually add flour, beating just until blended. Stir in pecans and vanilla.
3. Divide dough in half, and shape each portion into 2 (1 1/4-inch-thick) logs (about 12 inches long). Wrap in parchment paper, and cover and chill 1 hour or until firm.
4. Preheat oven to 325°. Cut logs into 1/4-inch-thick rounds, and place 1/2 inch apart on parchment paper-lined baking sheets.
5. Bake at 325° for 18 to 20 minutes or until lightly golden. Let cool on baking sheets 5 minutes. Transfer to wire racks, and let cool completely (about 20 minutes).