Prepare the pan Preheat the oven to 350°F or 175°C. Grease an 8×8 inch or 9×9 inch baking pan and line it with parchment paper. An 8×8 inch pan will produce a slightly thicker cake and it's what I used for this recipe.
Combine the dry ingredients In a medium bowl, whisk together the flour, salt, baking powder, cinnamon, nutmeg, ginger, and cloves.
Brown the butter Melt the butter in a small saucepan over medium heat. Continue cooking until it foams, smells nutty, and develops golden brown bits. Remove it from the heat and let it cool until it is no longer hot.
Mix the wet ingredients In a large bowl, combine the cane sugar, maple syrup, pumpkin puree, eggs, and vanilla. Add the cooled brown butter and beat with an electric hand mixer until creamy, fluffy, and slightly lighter in color.
Finish the batter Using the hand mixer on medium low, gradually beat the dry ingredients into the wet ingredients until just combined. The batter will be thick. Do not overmix. Fill the pan. Spread the batter evenly inside the prepared baking pan.
Add the crumble topping Combine the flour, brown sugar, cinnamon, and salt in a small bowl. Pour in the melted butter and mix with your fingers until crumbles form. If the mixture appears too wet, add a little more flour. Break the crumble into pieces and scatter it evenly over the cake batter.
Bake the cake Bake for about 45 minutes, or until the center is set and a toothpick comes out clean or with a few moist crumbs. If using a 9x9 pan, start checking at 40 minutes. Allow the cake to cool for 10 minutes before adding the drizzle.
Make the cream cheese drizzle Whisk together the powdered sugar, whipped cream cheese, vanilla, and water until smooth, thick, and pourable. Add another tiny splash of water or cream if needed. Drizzle over the cooled coffee cake before serving.