Preheat your oven to 350°F. Line an 8x8-inch square metal baking pan with parchment paper, leaving a small overhang on the sides for easy removal later, and grease heavily with butter.
For the cinnamon streusel topping: In a medium bowl, whisk together the ¾ cup flour, ⅓ cup brown sugar, ⅓ cup granulated sugar, 1 teaspoon vanilla extract, 1 tablespoon cinnamon, ½ teaspoon nutmeg, and ¼ teaspoon salt. Add the 6 tablespoons of cold, cubed butter. Work the butter into the dry mixture using a pastry cutter or your clean fingertips until it forms uniform, coarse crumbs. Place the bowl in the refrigerator to keep cold while you make the batter.
For the cake batter: In a medium bowl, whisk together the 1 ½ cups flour, 1 ½ teaspoons baking powder, and ½ teaspoon salt. Set aside. In a large mixing bowl (or stand mixer fitted with the paddle attachment), beat the softened ½ cup butter, ¾ cup granulated sugar, and ¼ cup brown sugar together on medium-high speed for 2 to 3 minutes until the mixture looks light, fluffy, and well creamed.
Add the eggs one at a time, beating well after each addition. Scrape down the sides of the bowl as needed. Beat in the 1 ½ teaspoons of vanilla extract until fully incorporated.
Alternate adding your ingredients to the bowl: Start with about one-third of the dry ingredients and mix well, then add half of the buttermilk and mix until incorporated. Add another third of the dry ingredients and mix again, add the rest of the buttermilk and mix again, and then finish with the remaining dry ingredients. Mix until just combined and no flour pockets remain.
Spread about half of the batter evenly into the bottom of your prepared 8x8 metal pan. Sprinkle half of the cinnamon streusel crumbs evenly over this initial layer of batter. Drop the remaining batter in small dollops carefully across the middle streusel layer. Using the back of a spoon or an offset spatula, gently smooth the dollops into an even layer without disturbing the crumbs beneath. Cover the top completely with the remaining half of the cinnamon streusel.
Bake at 350°F for 35 to 40 minutes. Check for doneness by inserting a toothpick into the center of the cake; it should come out clean or with a few moist crumbs. Remove from the oven and allow to cool completely in the pan on a wire rack.
For the icing: In a small bowl, whisk together the powdered sugar, vanilla extract, and 2 tablespoons of heavy cream. Add more cream a splash at a time if needed until smooth and drizzle consistency. Drizzle over the cooled coffee cake. Let the glaze set for a few minutes before slicing. Enjoy!