For rompope syrup:
Whisk all ingredients in medium bowl to blend. Pour half of liquid into heavy large saucepan. Bring to boil. Reduce heat to medium and boil gently until mixture is reduced to 1 1/4 cups, stirring frequently, about 17 minutes. Whisk in remaining half of liquid. (Can be made 1 day ahead. Rewarm just until lukewarm before using.)

For cake:
Preheat oven to 350°F. Butter and flour 8-inch-diameter cake pan with 2-inch-high sides. Line bottom of pan with parchment paper; butter and flour parchment. Whisk eggs and sugar to blend in large bowl. Set bowl over saucepan of simmering water (do not allow bottom of bowl to touch water). Using electric mixer, beat mixture constantly until thick, pale yellow, and tripled in volume, about 9 minutes. Remove bowl from over water. Continue to beat mixture until cool, about 6 minutes. Sift flour over egg mixture in 3 additions, gently folding in each addition. Transfer 1 cup batter to small bowl; fold in melted butter in 3 additions. Gently fold into batter in large bowl, being careful not to deflate batter. Transfer batter to prepared pan.

Bake cake until top is deep golden and tester inserted into center comes out clean, about 25 minutes. Cool cake in pan 10 minutes. Turn cake out onto deep platter at least 2 inches larger than cake. Remove parchment paper. Using wooden skewer, pierce cake all over top, spacing piercings 1/2 inch apart and pressing skewer down to bottom of cake.

Gradually pour half of lukewarm rompope syrup over top of hot cake, spreading over cake with spatula and allowing rompope syrup to soak into cake before adding more. Invert cake onto another large deep platter. Pierce cake all over top, spacing piercings 1/2 inch apart and pressing skewer down to bottom of cake. Gradually pour remaining rompope syrup over cake, spreading with spatula and allowing syrup to soak in before adding more. Let cake stand at room temperature until cooled completely, about 2 hours, occasionally spooning up any rompope syrup that collects on bottom of platter and drizzling syrup over cake. (Can be made 1 day ahead. Cover and refrigerate.)

For frosting:
Using electric mixer, beat cream and sugar in large bowl until peaks form. Spread frosting over cake. (Can be made 4 hours ahead. Cover and chill.) Garnish with halved berries and mint, if desired. Serve with sliced berries.