Hull and slice the strawberries into 1/2-inch thick pieces, then toss them with 4 tablespoons of sugar, lemon juice, and ground cinnamon in a baking dish. Roast at 400°F for 35-40 minutes, stirring halfway through, until the strawberries release their juices and become slightly caramelized at the edges. This roasting process concentrates the strawberry flavor and creates a natural syrup that will infuse the ice cream. Remove from the oven and stir in 2 teaspoons of vanilla, then let cool completely to room temperature.
While the strawberries cool, prepare your ice cream custard by whisking together the 5 egg yolks, 3.5 oz sugar, and salt in a heatproof saucepan. Heat this mixture over medium heat, stirring constantly, until it reaches 170°F (this takes about 10-12 minutes and pasteurizes the eggs). Once it reaches temperature, remove from heat and whisk in the 1 tablespoon vanilla, then add the milk and cream. I like to temper the egg mixture slowly with the cold dairy to avoid any scrambling—add the milk and cream gradually while whisking constantly.
Once the roasted strawberries from Step 1 have cooled completely, transfer half of them along with their syrup to a blender and puree until smooth. Strain the puree through a fine-mesh sieve if you prefer a smoother texture, though this is optional. Fold the strawberry puree into the custard base from Step 2, stirring until evenly combined. Cover and refrigerate overnight or for at least 8 hours—this resting period allows the flavors to meld and makes the mixture churn more efficiently.
Pour the chilled strawberry custard mixture from Step 3 into your ice cream maker and churn according to the manufacturer's instructions (typically 20-25 minutes) until it reaches a soft-serve consistency. Meanwhile, cut the sponge cake into 1/2-inch cubes. In a freezer-safe container, add about half of the churned ice cream, then layer with half of the whole roasted strawberries from Step 1 and half of the cake cubes. Top with the remaining ice cream, then finish with the remaining strawberries and cake cubes, creating a marbled effect. I find that slightly under-stirring the final layers helps keep the strawberries and cake visible throughout rather than becoming evenly distributed.
Cover the layered ice cream container and freeze for at least 4 hours, preferably overnight, until completely firm. This allows the ice cream to harden to the perfect scoopable consistency while the layers set. Serve with the cake and strawberry pieces featured prominently in each scoop.