Mash avocado in small bowl (should be chunky, not smooth). Add sun-dried tomatoes and half of garlic; mix well. Set aside.
Combine beef, remaining garlic, 2 tablespoons minced basil leaves and salt in medium bowl, mixing lightly but thoroughly. Lightly shape into four 1/2-inch thick patties.
Heat large nonstick skillet over medium heat until hot. Place patties in skillet; cook 10 to 12 minutes to medium (160°F) doneness, turning occasionally. Remove patties from skillet. Place buns, cut side down in skillet, cook 1 minute or until lightly toasted.
Place burgers on bottom of buns; top each with equal amounts avocado-tomato spread, fennel and remaining basil leaves. Close sandwiches.
Nutrition information per serving: 398 Calories; 162 kcal Calories from fat; 18 g Total Fat; 4 g Saturated Fat; 9 g Monounsaturated Fat; 76 mg Cholesterol; 898 mg Sodium; 32 g Total Carbohydrate; 10.1 g Dietary Fiber; 31 g Protein; 5.8 mg Iron; 9.3 mg Niacin; 0.7 mg Vitamin B6; 2.3 mcg Vitamin B12; 7.6 mg Zinc; 39.7 mcg Selenium; 98.6 mg Choline;