Preheat the oven to 350°F (175°C). Generously butter a 13x9-inch baking pan with the butter marked "butter, for greasing the pan."
In a medium bowl, whisk together 2½ cups all-purpose flour, 1 teaspoon baking soda, 1 teaspoon baking powder, and ½ teaspoon salt. Set this dry mixture aside.
In a large bowl or the bowl of a stand mixer, beat 10 tablespoons (1¼ sticks) unsalted butter (room temperature) and 1 cup granulated sugar until light and fluffy, about 3–4 minutes, scraping the sides of the bowl as needed.
Add the 3 large eggs to the butter-sugar mixture one at a time, beating briefly after each addition until incorporated. Mix in 1 teaspoon vanilla extract.
Add the reserved flour mixture to the wet ingredients, then add 1¼ cups sour cream. Beat just until combined and no large streaks of flour remain; do not overmix.
Scrape the batter into the prepared 13x9-inch pan and spread into an even layer with a rubber spatula.
Make the crumb topping: in a medium bowl, whisk together 3 cups all-purpose flour, 1 cup packed light brown sugar, 1 tablespoon ground cinnamon, and 1½ teaspoons coarse salt. Cut in 1¾ cups (3½ sticks) unsalted butter (room temperature) with a pastry blender, two forks, or a food processor (pulsing) until large, moist clumps form.
Sprinkle the crumb topping evenly over the batter, covering the surface.
Bake in the preheated oven until the top is golden brown and a toothpick inserted into the center comes out clean, 40–50 minutes. The center should feel slightly firm, not soft and soggy.
Remove the pan from the oven and transfer to a wire rack. Cool until warm or at room temperature, then slice and serve.