Spoon 1/3 cup lemon curd into small microwavable bowl. Microwave on High 10 to 15 seconds or just until softened. Measure 1 teaspoon into large bowl; reserve remaining lemon curd. In same large bowl, beat 1 cup granulated sugar, butter, lemon peel, vanilla and eggs with electric mixer on low speed 30 seconds. Beat on high speed 5 minutes, scraping bowl occasionally. Beat flour mixture into sugar mixture alternately with milk on low speed, beating just until smooth after each addition. Pour into pan.