Preheat the oven to 350°F (175°C). Line the baking pan with parchment paper for easy removal. In a large mixing bowl, whisk together the flour, sugar, baking powder, and salt.
Add the cold, cubed butter to the dry ingredients. Using a pastry cutter or fingertips, cut the butter into the mixture until it resembles coarse crumbs with small pea-sized pieces. This builds a flaky texture in the cake topping.
In a separate bowl, whisk together eggs, buttermilk, and vanilla extract until well combined. Pour the wet ingredients into the dry mixture and gently fold with a spatula until just combined. Do not overmix to keep the cake tender.
Gently fold the blueberries into the batter, ensuring even distribution without crushing the fruit. Transfer the batter to the prepared baking pan, spreading it evenly with a spatula.
Prepare the crumble topping by combining 2 tablespoons of flour and the coarse sugar. Sprinkle this evenly over the batter in the pan to create a crunchy, sweet topping.
Bake in the preheated oven for 35-40 minutes, or until the top is golden brown and a toothpick inserted into the center comes out clean. The edges may lift slightly, and the top will develop a crackled appearance.