Cook the bacon in a large skillet over medium heat until crisp, about 15 minutes. Drain on paper towels and cut in half; set aside.
Soft-boil the eggs: Bring a saucepan of water to a boil over medium-high heat. Lower the eggs into the water and cook exactly 6 minutes. Meanwhile, fill a bowl with ice water. Using a slotted spoon, remove the eggs from the boiling water and lower them into the ice water. Let sit at least 5 minutes, then peel.
Preheat a grill or griddle to medium high. Combine 1 tablespoon olive oil, the tomatoes, basil and garlic in a small bowl. Season with salt and pepper; toss 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 (the thickest part) of the head, creating a thick round disk. Lay the lettuce disk on a work surface and cut away the core. Slicing horizontally, cut the disk in half to create two 1/2-inch-thick round lettuce "steaks."
Whisk the remaining 2 tablespoons olive oil and the paprika in a small bowl; season with salt and pepper. Brush on both sides of the lettuce steaks; grill just to give the lettuce a little color on one side, about 30 seconds.
To assemble the salad, put a piece of grilled iceberg on each plate. Cut the soft-boiled eggs in half and arrange on top. Top with the avocado, bacon, radishes, onion and tomato mixture. Drizzle with olive oil and vinegar. Top with blue cheese and herbs; season with pepper.