Quarter 6 firm avocados; season with salt and pepper and brush with grapeseed oil. Grill over medium-high heat, turning, until marked all over, about 3 minutes.
Combine 3 tablespoons balsamic vinegar, 1 teaspoon Dijon mustard, 1/4 cup fresh parsley, 3 garlic cloves (crushed and quartered), 1/2 teaspoon salt and 1/8 teaspoon pepper in a blender. With the blender running, add 6 tablespoons olive oil and puree until smooth.
Drizzle the dressing over the avocados and garnish with more parsley.