Start by turning the oven to 350°F (175°C). Prepare a 9×13-inch baking pan by greasing it and lightly sprinkling with flour, or line it with parchment paper.
Take the softened butter and beat it with the caster sugar until it becomes light and airy. Add the eggs one at a time, making sure each is fully incorporated before adding the next. Stir in the vanilla extract.
In a separate bowl, mix the flour, baking powder, and salt. Add these dry ingredients to the butter mixture in portions, alternating with milk, beginning and ending with the flour. Stir until the batter is smooth, and then fold in the vegetable oil gently.
For the topping, mix flour, salt, cinnamon, brown sugar, and white sugar in another bowl. Work in the softened butter with a fork or pastry cutter until the mixture looks like coarse crumbs.
Pour the batter into the pan and smooth the surface. Sprinkle the crumb mixture evenly over the top. Place the pan in the oven and bake for 45–50 minutes. Check by inserting a toothpick into the center; it should come out clean.
Let the cake rest in the pan for about 10 minutes before moving it to a wire rack to cool completely. Once cooled, cut into slices and enjoy.