**Preheat** your oven to 350°F.
**Butter** an 8-inch by 8-inch baking dish.
**Line** the dish with parchment paper, allowing two edges to hang over the sides.
In a medium bowl, mix 1/2 cup brown sugar, 1/4 cup flour, 1 teaspoon cinnamon, and 1/8 teaspoon salt. Add 1 teaspoon vanilla extract and 4 tablespoons chilled butter, working it in until pea-sized clumps form. Refrigerate the crumble topping.
In another bowl, combine 2 cups flour, 2 teaspoons baking powder, 1 teaspoon cinnamon, and 1 teaspoon kosher salt. Set aside.
In a small bowl or large measuring cup, mix 1/2 cup milk with 1/2 cup yogurt until thoroughly combined. Set aside.
In the bowl of a stand mixer, beat 1 stick of softened butter, then add 3/4 cup granulated sugar, 1 egg, and 1 teaspoon vanilla extract. Scrape down the sides and beat again.
Gradually add the flour mixture and milk mixture alternately, beating just until combined. Fold in one package of raspberries gently.
Dollop the batter into the prepared baking dish, smooth the top, and sprinkle the crumble topping over it. Drop half of the remaining raspberries over the crumble.
Bake for 45–50 minutes or until a toothpick inserted in the center comes out clean.
Allow to cool for 5 minutes in the baking dish. Lift the cake from the dish using the parchment paper edges and transfer to a wire rack to cool for an additional 5-10 minutes or until safe to cut.
Cut the coffee cake into eight servings and garnish with the remaining raspberries.
Serve the Raspberry Crumb Coffee Cake warm or at room temperature. Enjoy!