Step 1: For the Streusel: In a medium bowl, combine flour, granulated sugar, brown sugar, and cinnamon. Add cold, cubed butter. Cut in with a pastry blender or fingertips until mixture resembles coarse crumbs. Refrigerate while preparing the cake.
Step 2: For the Pumpkin Coffee Cake: Preheat oven to 350°F (175°C). Grease and flour a 9×13 inch baking pan.
Step 3: In a large bowl, whisk together flour, granulated sugar, brown sugar, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt.
Step 4: In a separate medium bowl, whisk together pumpkin puree, melted butter, eggs, milk, and vanilla extract until smooth.
Step 5: Pour the wet ingredients into the dry ingredients. Mix with a spoon or spatula until just combined. Do not overmix.
Step 6: Pour batter into the prepared baking pan and spread evenly. Sprinkle the chilled streusel topping over the batter.
Step 7: Bake for 35-45 minutes, or until a wooden skewer inserted into the center comes out with moist crumbs. Let cool completely on a wire rack.
Step 8: For the Cream Cheese Icing: In a medium bowl, beat softened cream cheese and butter with an electric mixer until smooth and creamy.
Step 9: Gradually add powdered sugar, vanilla extract, and a pinch of salt. Beat until light and fluffy. If too thick, add milk 1 teaspoon at a time until desired drizzling consistency is reached.
Step 10: Once the cake is completely cool, drizzle or spread the cream cheese icing over the top. Slice and serve.