Preheat oven to 350°F and spray a 13 x 9-inch baking dish with nonstick spray. Whisk together cake flour, baking powder, baking soda, and salt in a medium bowl.
Beat butter, sugar, and vanilla in a large mixer bowl on medium speed until pale and fluffy. Add eggs one at a time and beat until thoroughly incorporated. Combine buttermilk and yogurt in a small bowl. Reduce speed to low and add flour mixture in 3 additions, alternating with buttermilk mixture (begin and end with flour mixture). Beat just until smooth; pour batter into prepared baking dish and smooth with an offset spatula.
For the streusel, whisk together oats, brown sugar, and cinnamon in a small bowl. Heat cookie butter in a microwave-safe bowl until melted, about 30 seconds. Stir into oatmeal mixture until large clumps form. Scatter streusel evenly over batter.
Bake for 23 to 25 minutes, until a toothpick inserted in the center comes out with just a few crumbs attached and cake begins to pull away from edges of the pan. Cool completely in pan on a wire rack before cutting into squares.
Store leftovers in an airtight container at room temperature up to 2 days.
Notes
*Make your own cake flour: place 2 tablespoons cornstarch in an empty 1-cup measure, then top up with flour. Sift the mixture several times to evenly distribute the cornstarch.