1. Preheat grill to 350 degrees Fahrenheit. Combine paprika, cayenne pepper, black pepper, garlic powder, onion powder, oregano and thyme in a small bowl.
2. Slice off the top of the onions. (Not the root! That’s what’s going to anchor your onion.) Make a shallow slit down the side of the onion and peel off the outer layers. Place the onion on a cutting board, cut side down, and slice, starting about 1/2 inch away from the root, all the way down. Start with four even sections, and then divide each section evenly two to three times. Flip the onion, carefully separate the petals, and set aside. Repeat with remaining onions.
3. Drizzle onions with olive oil and season with spice mixture. Place onions, root side down, onto the grill. Close the grill and cook for 30-35 minutes.
4. While onion is grilling, make the sauce by mixing Thousand Island dressing and horseradish sauce.
5. Remove onion blossoms from the grill and serve warm with dipping sauce.