Combine feta cheese and Greek yogurt in a food processor. Process for a few minutes until smooth, using a spatula to scrape down the sides as needed.
To the food processor, add pumpkin puree, 1 to 2 Tbsp honey (adjust to preferred sweetness), thyme, and a few cracks of black pepper. Process again until all ingredients are thoroughly incorporated.
Move the whipped feta into a container, cover, and chill in the refrigerator for 30 to 60 minutes to set and cool.
For serving, place the chilled whipped feta in a large bowl. Top with a handful of chopped walnuts (if using), a generous sprinkle of fresh thyme, an additional drizzle of honey, and more black pepper.
Accompany with crusty toasted bread or crackers for dipping.