Coat a 15 x 10-inch jelly-roll pan or a 9-inch springform pan with cooking spray; line with wax paper. Coat paper with cooking spray; dust with 1 tablespoon flour. Set aside.
Cook butter in a small saucepan over medium heat until lightly browned (about 4 minutes).
Pour into a small bowl; cool and set aside.
Lightly spoon 1 cup flour into a dry measuring cup; level with a knife.
Combine 1 cup flour and salt in a sifter. Sift the flour and salt once; set aside.
Beat sugar, vanilla, and eggs at high speed of a mixer until ribbons fall from beaters (about 10 to 15 minutes or until the egg mixture holds its shape). Lightly spoon one-third of flour mixture onto egg mixture; quickly fold. Repeat procedure twice with remaining flour mixture.
Stir about 1 cup batter into cooled browned butter. Gently fold butter mixture into remaining batter. Spoon batter into prepared pan; spread evenly.
Bake in jelly-roll pan at 375 for 12 minutes or in springform pan for 20 minutes, or until a wooden pick inserted in center comes out clean or the cake springs back when touched lightly in center. Loosen from sides of pan; turn out onto a wire rack. Carefully peel off wax paper. Cool completely.
