Preheat oven to 375 degrees. Spray two 8-inch round cake pans with cooking spray, line each with a parchment paper round, and spray again. Set pans aside.
Beat butter in the bowl of an electric mixer fitted with the paddle attachment. Gradually add 1 cup sugar and continue to beat until mixture is light and fluffy. Beat in syrup.
In a medium bowl, sift together flour, baking powder, and salt. Mix flour mixture into butter mixture, alternating with milk, beginning and ending with flour mixture.
Beat eggs until foamy in another bowl of an electric mixer fitted with the whisk attachment. Add remaining 1/4 cup sugar and continue beating until thickened, about 5 minutes. Stir into cake batter until well combined.
Divide cake batter evenly between prepared pans. Bake until cakes spring back when gently touched in the center, about 25 minutes. If cakes do not spring back, return to oven and continue cooking about 10 minutes more.
Cool cake in pans for 10 minutes. Invert cakes onto a wire rack and remove parchment paper round. Let cakes cool to room temperature before frosting.
Place four strips of parchment paper around perimeter of a serving plate or lazy susan. Place the first layer on the cake plate. Spread the top of the first layer with frosting. Top with the remaining layer, bottom-side up. Spread entire cake with frosting; remove parchment paper strips. Serve cake drizzled with any remaining caramel syrup.