Dry the feta: Pat the block of feta dry with paper towels to remove excess brine. Extra moisture is the main reason this dip can turn out watery instead of fluffy.
Combine the base: Add the feta, cream cheese, pumpkin puree, olive oil, and garlic to a food processor. Pulse several times until the mixture looks mostly smooth, about 1 minute.
Add the spices: Sprinkle in the cinnamon, smoked paprika, cayenne, and salt. Blend again until the dip turns pale orange and takes on a light, whipped texture, about 30 seconds.
Sweeten to taste: Drizzle in the honey and pulse briefly to combine. Taste and add a touch more honey or salt if needed.
Scrape and check texture: Stop the processor and scrape down the sides with a spatula. Pulse once more to make sure everything is evenly blended with no large feta chunks left.
Chill the dip: Transfer the dip to a serving bowl and refrigerate for at least 20 minutes. This short rest helps the flavors settle and firms up the texture slightly.
Garnish: Just before serving, drizzle the top with a little olive oil or extra honey. Sprinkle with chopped parsley or chives for color.
Serve: Serve the dip slightly chilled or at room temperature alongside warm pita, crackers, or sliced apples.