Cook the bacon slices in a medium skillet until crisp. Drain on paper towels and halve the slices crosswise; set aside.
Preheat a gas grill or stovetop griddle to medium-high heat.
In a small bowl, toss together 1 tablespoon of the olive oil, the tomatoes, basil and garlic; season with salt and pepper, toss to combine and set aside.
Stand the iceberg head upright on the core. With a sharp knife, cut a 1-inch-thick slice out of the center (thickest part) of the lettuce head, creating a thick, round disc. Lay the lettuce disc on a work surface and cut away the core. Slicing horizontally, cut the disc in half again, creating two 1/2-inch-thick round lettuce "steaks."
In a small bowl, whisk together the remaining 2 tablespoons oil and the paprika, and season with salt and pepper. Brush both sides of the lettuce steaks with the oil mixture and grill just to give the lettuce a little color, about 30 seconds on each side.
To assemble the salad, put the grilled iceberg discs on 2 serving plates. Slice the top and bottom of each egg so it will stand upright, and halve each crosswise; set 3 egg halves upright on each lettuce disc. Arrange 6 wedges of avocado and 6 pieces of bacon on each disc, pointing inward and stacking them on top of each other. Scatter the radish slices and onion rings evenly over each salad and divide the tomatoes between each, scattering them over the top. Drizzle a little olive oil and the red wine vinegar over each salad and onto the plate. Sprinkle the blue cheese over the top of the salads and onto the plate and garnish each with a sprinkling of chopped herbs. Serve immediately.
Bring a medium saucepan of water to a boil over medium-high heat. Lower the eggs into the water and cook for exactly 6 minutes. (Note: It is imperative that the eggs are at room temperature before cooking them to achieve the right consistency with this method.)
Meanwhile, fill a bowl with ice water. Using a strainer or slotted spoon, remove the eggs from the boiling water and lower them into the ice water. Let stand for at least 5 minutes; peel. When sliced, the eggs should have firm whites with runny yolks that are just beginning to set.