Allow eggs to stand at room temperature 30 minutes. Meanwhile, grease and flour three 8 1 1/2-inch round baking pans. In a bowl combine flour, baking powder, and salt; set aside.
Preheat oven to 350 degrees F. In an extra-large bowl beat eggs with a mixer on high 5 minutes or until thickened and light. Beat on medium an additional 5 minutes while gradually adding sugar, 1/4 cup at a time. (Batter will be light and fluffy.) Beat in flour mixture on medium-low until just combined.
In a small saucepan heat and stir milk and butter until butter melts. Add to batter, beating until combined; beat in almond extract. Divide batter among prepared pans.
Bake 25 minutes or until a wooden toothpick inserted near centers comes out clean. Transfer pans to a wire rack; cool 10 minutes. Remove cakes from pans; cool completely on wire racks over a shallow pan or tray. Using a long-tine meat fork, poke cakes all over. Slowly pour Prosecco over cakes. Wrap in plastic wrap; chill 2 to 24 hours.
Fresh peach filling
In a large bowl combine peaches, Prosecco, and sugar; stir well. Let stand, covered, 30 minutes, stirring occasionally. Using a potato masher or fork, mash into a coarse mixture.
Whipped cream frosting
In an extra-large bowl beat heavy cream, sour cream, sugar, and vanilla with mixer on medium until stiff peaks form; set aside.
Place one cake layer on a serving plate. Spread with half the fresh peach filling. Top with second cake layer; spread with remaining peach filling. Top with third cake layer. Spread top and sides with frosting. To serve, top with sliced peaches and mint leaves.