Preheat the oven to 350°F. Grease a 9-by-13-inch pan and line it with parchment paper. Lightly grease the parchment paper.

Pour the prepared lemon cake batter into the pan. Bake until a toothpick inserted into the center comes out clean, 20 to 25 minutes.

While the cake bakes, combine the blueberries, ¼ cup water and sugar in a small pot. Bring to a simmer over medium heat until the mixture becomes juicy, about 5 to 6 minutes.

In a small bowl, mix the cornstarch with a small amount of the hot blueberry liquid. Whisk to combine, then pour the cornstarch mixture back into the pot. Continue to simmer until the blueberry mixture thickens slightly, 2 to 3 minutes more. Stir in the vanilla extract.

Let the cake cool for 7 minutes. Using the handle of a wooden spoon, poke holes into the cake, leaving at least ¾ inch between each hole.

Pour the warm blueberry syrup over the cake. Use a spatula to spread it evenly and also encourage it into the holes. Cool the cake completely.

In the bowl of an electric mixer fitted with the whisk attachment, whip the heavy cream to soft peaks. Add the confectioners' sugar and lemon zest and then whip to medium peaks.

Spread the whipped cream evenly over the cooled cake. To serve, slice into squares. If not serving immediately, cover and refrigerate. The cake will keep for 2 days.