Add the blueberries, sugar, and lemon juice to a large saucepan. Cook over medium-high heat, stirring occasionally, until the blueberries release their juices and the mixture comes to a boil.

Reduce the heat to medium-low. Continue cooking for 25 to 35 minutes, stirring occasionally and gently crushing the berries as they soften. The mixture should reduce, darken, and become noticeably thicker.

Remove the pan from the heat. Carefully blend the mixture with an immersion blender until smooth. Alternatively, transfer it to a blender and blend until smooth, working carefully because the sauce will be hot.

Pour the sauce through a fine-mesh strainer, pressing firmly with a spatula to extract as much liquid and pulp as possible. Discard the skins and seeds left in the strainer.

Return the strained sauce to the saucepan.

Mix the cornstarch and water in a small bowl until smooth. Add the slurry to the blueberry sauce and cook over medium heat, stirring constantly, until the sauce comes to a gentle boil and thickens, about 1 to 2 minutes.

The finished sauce should be thick enough to spread without immediately running off a spoon. It will thicken further as it cools.

Transfer the sauce to a bowl. Place plastic wrap directly against its surface and let it cool to room temperature. Refrigerate for several hours, or until completely cold.

Reserve ½ cup for the Chantilly frosting. The remaining sauce will be used to cover the cake.

Preheat the oven to 350°F (180°C). Grease a 9 × 13-inch metal baking pan and line the bottom with parchment paper.

Wash the blueberries and dry them thoroughly. Set aside.

In a medium bowl, whisk together the flour, cornstarch, baking powder, baking soda, and salt.

In the bowl of a mixer, beat the butter for one minute. Add the sugar and beat for another 3 minutes, until light and fluffy.

Add the oil and mix until incorporated.

Add the eggs one at a time, mixing well after each addition. Add the vanilla along with the last egg.

Add the sour cream and mix until combined.

Add the dry ingredients in three additions, alternating with the milk in two additions. Begin and end with the dry ingredients, mixing on low speed after each addition just until combined. Do not overmix.

Spread about half of the batter evenly into the prepared pan. Scatter 1 cup of the blueberries over the batter.

Spoon the remaining batter over the blueberries and gently spread it into an even layer. Scatter the remaining ½ cup blueberries over the top, then press them lightly into the batter so they are mostly covered.

Bake for 40 to 45 minutes, or until the center springs back when gently pressed and a toothpick inserted into an area without a blueberry comes out clean or with a few moist crumbs. The internal temperature in the center should register about 205°F (96°C).

Remove the cake from the oven and let it cool in the pan for at least 30 minutes.

Whisk together the whole milk and sweetened condensed milk.

Once the cake is mostly cool, poke holes all over it with a fork or wooden skewer.

Slowly pour the milk mixture evenly over the cake, allowing it to soak into the holes. Use a brush to help spread it evenly.

Cover the cake and refrigerate overnight.

Spread the remaining blueberry sauce evenly over the chilled, soaked cake.

Return the cake to the refrigerator for 20 to 30 minutes. This will help keep the blueberry layer distinct beneath the frosting.

Beat the softened butter for thirty seconds. Add the cream cheese and beat for about 1 to 2 minutes, until completely incorporated. Scrape the bottom and sides of the bowl well to remove any lumps.

Add the powdered sugar and vanilla extract. Beat on medium speed until smooth and slightly fluffy.

Add the cooled blueberry jam and mix until evenly combined.

In a separate clean bowl, whip the very cold heavy cream until it holds medium-firm peaks. Do not overwhip.

Add about one-third of the whipped cream to the blueberry cream cheese mixture and gently fold until mostly combined. Fold in the remaining whipped cream in two additions, using a spatula and taking care not to deflate it.

Continue folding just until the frosting is smooth, fluffy, and evenly combined. Use immediately.

Carefully spoon the blueberry Chantilly frosting over the sauce. Spread it gently into an even layer, taking care not to mix it into the blueberry sauce underneath.

Arrange fresh blueberries over the frosting.

Refrigerate for at least 1 hour before serving. However, if the cake has been in the fridge for over a couple of hours, let it sit on the counter for thirty minutes before serving for best consistency.