Meanwhile, heat 4 tablespoons oil in a 10 to 12-inch saute pan until smoking. Add garlic and sundried tomatoes and cook until light golden brown. Add bread crumbs and continue cooking until well mixed. Remove from heat and allow to cool. Add thyme, scallions and parsley and stir to mix.
Stuff cool calamari and season with salt and pepper. Brush stuffed calamari and tentacles with 1 tablespoon olive oil and place on grill. Cook until nicely barbecued, about 10 minutes, turning once.