3 large eggs
1 3/4 cups plus 3 tablespoons sugar, divided
1/2 teaspoon vanilla extract
2 tablespoons vegetable oil
1/2 cup whole milk
1 tablespoon sour cream
1 1/2 tablespoons plus 1 teaspoon lemon zest, divided
1 1/2 tablespoons fresh lemon juice
1 1/2 teaspoons honey
1 cup all-purpose flour
1 1/2 teaspoons baking powder
1/2 teaspoon plus 1/3 teaspoon kosher salt, divided
1 1/2 pints strawberry gelato, softened slightly
1 1/2 pints pistachio gelato, softened slightly
1/3 cup water
3 large egg whites
Preheat oven to 350°. Spray 1 (8-inch) round cake pan with baking spray with flour; line bottom of pan with parchment paper.
In the bowl of a stand mixer fitted with the whisk attachment, beat eggs, 3/4 cup sugar, and vanilla at medium-high speed until pale yellow and fluffy, about 4 minutes. Reduce mixer speed to medium, and slowly add oil, beating until combined.
In a medium bowl, whisk together milk, sour cream, 1 1/2 tablespoons zest, lemon juice, and honey. In a small bowl, whisk together flour, baking powder, and 1/2 teaspoon salt.
With mixer on low speed, gradually add flour mixture to egg mixture alternately with milk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Add batter to prepared pan. Tap pan on counter to release air bubbles.
Bake until a wooden pick inserted in center comes out clean, 25 to 35 minutes. Let cool in pan for 15 minutes. Remove from pan, and let cool completely on a wire rack.
Spray 1 (2-quart) metal bowl with cooking spray. Add strawberry gelato, and use a rubber spatula to firmly press gelato into bowl. Layer pistachio gelato. Press cake into prepared bowl. Cover bowl with plastic wrap, and freeze overnight.
Turn cake out onto a flat plate. Use a kitchen torch to heat outside of bowl slightly until cake is fully inverted onto plate. Return to freezer.
In a medium saucepan, combine 1/3 cup water and 1 cup plus 1 tablespoon sugar. Cook over high heat until a candy thermometer registers 240°. Transfer sugar syrup to a heatproof pitcher; let cool until no more bubbles are visible.
In the bowl of a stand mixer fitted with the whisk attachment, beat egg whites and remaining 1/3 teaspoon salt at medium speed until foamy. Add remaining 2 tablespoons sugar and remaining 1 teaspoon zest, beating until combined.
Increase mixer speed to high, and slowly pour in sugar syrup; beat until a stiff meringue forms. Using a rubber spatula, cover cake and gelato with meringue. Use a kitchen torch to toast meringue. A completed Baked Alaska will hold in freezer for up to 12 hours.