In a large mixing bowl, whisk together the flour, sugar, baking powder, cinnamon, nutmeg, cloves, and salt until well combined.
In a separate bowl, stir together the pumpkin puree, eggs, milk, and vanilla until smooth and slightly frothy.
Pour the wet mixture into the dry ingredients and gently fold with a spatula until just combined; the batter will be thick and slightly sticky.
Heat oil in a deep fryer or heavy-bottomed pot over medium heat until it reaches 350°F (175°C).
Lightly flour your hands and carefully shape the dough into small balls or use a donut cutter to form rings, then carefully place them into the hot oil.
Fry the donuts in batches, turning occasionally, until they are golden brown and cooked through, about 3-4 minutes per batch.
Use a slotted spoon to remove the donuts and transfer them to a cooling rack lined with paper towels to drain excess oil.
In a shallow dish, mix together the cinnamon and sugar. Once the donuts are cool enough to handle, roll or dip them in the cinnamon sugar mixture to coat evenly.
Place the coated donuts on a rack for a few minutes to set the coating and allow the exterior to become slightly crisp.
Transfer the finished donuts to a serving plate and enjoy their warm, aromatic aroma and soft, moist interior.