Whisk together first 9 ingredients in a medium bowl, whisking until smooth; add salt and pepper to taste.
Coat cold grill grate with cooking spray. Preheat grill to 350° to 400° (medium-high) heat. Lightly coat cut sides of avocados and lettuce with cooking spray; season with salt and pepper. Grill avocado halves and lettuce, cut sides down and covered with grill lid, 1 minute or until grill marks appear.
Slice avocados. Chop lettuce, and arrange on a platter. Top with avocado, radishes, and blue cheese. Drizzle with dressing. Add salt and pepper to taste.
The buttermilk dressing that goes with this salad is DIVINE! Add grilled avocados and I've died and gone to heaven! I didn't grill the lettuce and it was just fine. I'm thinking about using Bibb lettuce the next time I make this. My husband and I fought over the leftovers. There is no reason to ever buy bottled dressing. You can make dressing yourself that rivals the finest restaurants!
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