Let’s create this spectacular Sheet Pan Ice Cream Cake:

1. Prepare Oven and Bake the Sheet Pan Cake:

• Position an oven rack in the center of the oven and preheat to 375°F (190°C).
• Lightly coat an 18-by-13-inch sheet pan with nonstick baking spray. Line the bottom with parchment paper.
• In the bowl of a stand mixer fitted with a whisk attachment, beat the 4 cold eggs, 1 cup of sugar, 1 teaspoon baking powder, and 1 teaspoon kosher salt on high speed for about 10 minutes. The mixture should become very thick, pale in color, and hold a ribbon-like “wake” from the whisk when lifted. This step is crucial for the cake’s structure.
• Reduce the mixer speed to medium-high and slowly drizzle in the melted and cooled butter and the vanilla extract, mixing just until combined, about 10 seconds.
• Reduce the speed to low and add the sifted all-purpose flour all at once. Beat for just a few seconds (about 5 seconds) until just combined. Do not overmix!
• Gently fold the batter once or twice with a rubber spatula to ensure no flour pockets remain. Scrape the batter into the prepared sheet pan and spread it evenly with the spatula, using broad, gentle strokes to maintain its airiness.
• Bake, rotating the pan halfway through, for 15 to 18 minutes, until the top is lightly golden and a toothpick inserted into the center comes out clean.
• Transfer the pan to a wire rack and allow the cake to cool completely in the sheet pan.

2. Prepare Ice Cream and Cake Layers for Assembly:

• Remove the three pints of ice cream (chocolate, vanilla, strawberry) from the freezer about 15 minutes before you are ready to assemble the cake, allowing them to soften slightly to a spreadable consistency.
• Once the sheet pan cake is completely cool, use a sharp paring knife to cut the cake into 3 long rectangles, approximately 9 ½-by-4 ½ inches each (to fit your 10×5 loaf pan).
• Reserve the remaining cake trimmings for the final top layer.

3. Prepare Loaf Pan and Assemble the Cake:

• Line the inside of a 10-by-5-by-3-inch loaf pan with plastic wrap, leaving enough overhang on all sides to cover the top of the pan later.
• Layer 1: Place one cake rectangle in the bottom of the plastic-wrap-lined loaf pan, gently pushing it down to fit and trimming the edges as needed. Spread the softened chocolate ice cream evenly over the cake layer using a small offset spatula.
• Layer 2: Place the second cake rectangle on top of the chocolate ice cream. Gently press down. Spread the softened strawberry ice cream evenly over this cake layer.
• Layer 3: Place the third cake rectangle on top of the strawberry ice cream. Gently press down. Spread the softened vanilla ice cream evenly over this cake layer.
• Top Layer: Use the reserved cake trimmings to create the final top layer, cutting them to fit like a puzzle and pressing gently to create a solid surface.

4. Freeze the Assembled Cake:

• Cover the top of the cake with the overhanging plastic wrap, sealing it well.
• Place the loaf pan in the freezer and freeze until completely firm and solid, at least 4 hours, but preferably up to 12 hours or overnight.

5. Make Chocolate Shell and Unmold:

• When ready to serve, prepare the chocolate shell. Place the finely chopped semi-sweet chocolate and coconut oil in a small, microwave-safe glass bowl. Microwave in 20-second intervals, stirring with a rubber spatula after each interval, until completely melted and smooth. Set aside for a moment.
• Remove the loaf pan from the freezer. Uncover the top. Let it sit at room temperature for about 5 minutes to make unmolding easier.
• Invert the loaf pan onto a serving platter. Lift the pan off. Gently peel the plastic wrap away from the cake. (If it doesn’t release, gently tug on the plastic wrap to help lift the cake from the pan).

6. Garnish and Serve:

• Pour the melted chocolate shell over the top of the frozen ice cream cake, allowing some to drip decoratively down the sides.
• The chocolate shell will harden quickly on the cold cake.
• Slice the ice cream cake immediately with a long, sharp knife (run under hot water for clean cuts) and serve.

The careful layering and freezing are what make this cake so impressive!