Step 1Wash, stem and slice the strawberries. Place 2/3 of them into a blender with 1/4 cup of the sugar and the lemon juice. Blend until smooth. Set aside.
Step 2Combine the egg yolks and remaining sugar in a medium bowl and whisk until thick and pale yellow, about 3 minutes. Set aside.
Step 3Heat the cream and milk in a large saucepan over medium heat just until bubbles begin to form around the edges, about 5 minutes. Pour about 1 cup of the hot milk mixture into the sugar and egg yolk mixture while stirring constantly. Return it to the milk mixture and cook over low heat, stirring constantly, until the mixture coats the back of a spoon, about 4 minutes.
Step 4Let the hot liquid cool about 5 minutes, then stir in the pureed strawberries. Let cool to room temperature, then freeze according to the instructions with your ice cream maker.
Step 1While the ice cream is freezing, coat the stemmed strawberries with the chocolate coating, then refrigerate.
Step 2Cut a very thin slice (about 1/4 inch) horizontally from the top of the cake. Set the top aside.
Step 3Working with a small sharp knife, carefully hollow out a "trench" in the middle of the cake about 3/4 inch from the sides; discard the part of the cake you cut out. Spoon or pipe the ice cream into the trench until it is even with the cake. (You will have leftover ice cream that can be served with the cake.) Layer the remaining sliced strawberries over the ice cream. Replace the top of the cake, wrap it well and freeze until solid, at least 2 hours or overnight.
Step 4Remove the cake from the freezer and let it sit at room temperature, 30 minutes. Meanwhile, whip the cream and the powdered sugar until stiff peaks form, about 3 minutes. Remove the top from the cake and pipe about 1/3 of the whipped cream on top of the strawberries. Replace the top, then pipe the remaining cream on top of the cake and decorate it with the chocolate-covered strawberries.