Preheat the oven to 350°F.

Whisk the flour, cane sugar, cornstarch, ground fennel, baking powder, baking soda, and salt in a large bowl until the mixture is uniform.

Stir the milk, applesauce, oil, lemon juice, zest, vanilla, and water together in a separate bowl and let the mixture rest for a few minutes—it may look curdled, which is expected.

Grease an 8-inch round cake pan with oil and line the bottom with parchment paper.

Pour the wet mixture into the dry ingredients, folding gently with a spatula until just combined; it is fine if some small lumps remain, but do not overmix or the cake will be dense.

Toss the blueberries with the tablespoon of flour in a medium bowl until they are evenly coated, which helps prevent them from sinking during baking.

Spread half of the batter into the prepared pan and sprinkle with half of the blueberries. Layer the remaining batter and berries on top, adding a sprinkle of raw sugar if you want a crunchy lid.

Bake until the top is golden brown and a toothpick inserted into the center comes out clean, about 45 to 50 minutes.

Rest the cake in the pan for 5 minutes, then move it to a cooling rack for at least 1 hour to allow the crumb to set before serving.