Bring 4 qt. water to a boil in an 8-qt. stockpot. Add greens; cook 30 seconds. Remove greens, and pat dry with paper towels.

Process greens, walnuts, and next 3 ingredients in a food processor 2 to 3 minutes or until a paste forms, stopping to scrape down sides. With processor running, pour oil and lemon juice through food chute in a steady stream, processing until smooth. Add honey and cheese, and pulse 3 or 4 times or until blended. Add kosher salt and black pepper to taste. Serve immediately, or place plastic wrap directly on pesto (to help retain color), and refrigerate up to 1 week. Let stand 10 minutes before serving.

Note: We tested with Glory Turnip Greens.