Leave root and 1-inch stem on beets; scrub with a brush. Place in a 6-quart pressure cooker; add 2 1/2 cups water. Close lid securely; bring to high pressure over high heat. Reduce heat to medium or level needed to maintain high pressure; cook 10 minutes. Remove from heat; let stand for 6 minutes. Release pressure through steam vent, or place cooker under cold running water to release pressure. Remove lid. Drain and rinse beets with cold water. Drain; cool. Trim off beet roots; rub off skins. Cut beets in half vertically; cut each half into 4 wedges. Place in a medium bowl.
Combine vinegar and next 5 ingredients (through pepper) in a small bowl; stir with a whisk. Slowly drizzle in oil, stirring constantly with a whisk until well combined. Toss oil mixture with beets; let stand 15 minutes, tossing gently occasionally. Stir in dill. Top with walnuts just before serving.
Put 1/2 inch of water into a flat bottom bowl, poked holes in the beets and microwaved whole on high for 5.5 minutes. The dill is a must in this recipe - tasted the sauce before and after and there is a huge difference. Peeled and cubed the beets (the better to get more yummy sauce). Very happy with result - instant hit.