Heat your oven to 350°F and position a rack in the center. Grease a 9x13 inch baking pan (or similar size) with butter or cooking spray, making sure to coat the bottom and all sides evenly to prevent sticking. This prepares your pan while you move into the mixing phase.

Shred your zucchini and place it in a clean kitchen towel or several layers of paper towels. Squeeze firmly to remove excess moisture—this is crucial to prevent a wet cake. Set the dried zucchini aside. While this drains, beat the softened cream cheese and butter together in a large bowl until light and fluffy, about 2-3 minutes. Add the sugar gradually and mix well until combined.

Add the eggs one at a time to the wet mixture from Step 2, beating well after each addition. Pour in the vanilla extract and beat the mixture for 3 minutes total—this incorporates air for a tender crumb. Blend in the applesauce, which adds moisture while keeping the cake light. The batter should look smooth and creamy at this point.

In a separate bowl, whisk together the flour, baking soda, baking powder, and salt—this distributes the leavening agents evenly. I like to sift the flour first if it's been stored a while, as it can become compacted. Add the dry mixture to the wet batter from Step 3 and fold gently with a spatula until just combined. Overmixing can lead to a tough cake, so stop as soon as you see no visible flour streaks.

Fold the prepared zucchini from Step 2, strawberry topping, and finely chiffonaded basil into the batter from Step 4 until everything is evenly distributed. Pour the batter into your prepared pan from Step 1 and smooth the top with a spatula. Bake in the preheated 350°F oven for 45-50 minutes, until a toothpick inserted in the center comes out clean or with just a few moist crumbs.

Remove the cake from the oven and let it cool in the pan for 30 minutes—this allows the structure to set without it cracking as it cools. After 30 minutes, turn the cake out onto a wire cooling rack and allow it to cool completely to room temperature before glazing, about another 30-45 minutes.

While the cake cools, prepare the strawberry-basil glaze by whisking together the sifted confectioners sugar, milk, strawberry topping, fresh basil, and lemon zest in a small bowl until smooth and pourable. I find that sifting the confectioners sugar first eliminates lumps and gives you a silkier glaze every time. Pour or drizzle the glaze evenly over the completely cooled cake, allowing it to cascade down the sides naturally. Let the glaze set for about 15 minutes before serving.