In a large mixing bowl, cream together softened butter and granulated sugar for 3-5 minutes. The mixture should go past the stage where it is crumbly, and become very fluffy, smooth, and light in color.
Add the pumpkin purée into the mixture and beat until incorporated.
To the same bowl, add flour, baking powder, salt, cinnamon, cloves, nutmeg, milk, and vanilla extract.
Beat together until it is almost fully mixed, but there's still a bit of the dry mixture visible. At this point I like to swap to a rubber spatula to help ensure that I don't over-mix. Fold the batter until everything is just combined, and there is no more dry flour. The batter will be quite thick and fluffy.
Transfer the batter to your prepared 8x8" pan and spread about half of it out in an even layer. (I like to use an offset spatula for this but a rubber spatula works fine too.)
Take the streusel topping from the fridge and use your hands to crumble about half of it over the top of the batter in an even layer.
Top the streusel with the remainder of the batter and spread it in another even layer. It can be a little tricky to spread the batter over the first layer of streusel. It can be helpful to dollop the batter around the pan first so you're not spreading it all out from one spot. Then gently spread.
Add the remainder of the streusel topping to the top of the coffee cake.
Bake in a preheated oven for 40-50 minutes — this can vary quite a bit oven-to-oven. If you gently shake the pan, the center should be completely set (not jiggly at all). A knife/toothpick inserted into the center should come out clean or with only a few moist crumbs. Lastly, the streusel topping should be crisp and not soggy — if it still looks wet, cook for an extra 5 minutes and check again.
The cake will be a bit gummy if you cut into it right away. I recommend allowing it to cool in the pan for about 30 minutes before enjoying.