Place the garlic in a food processor, and pulse. Add the parsley, basil, 5 tablespoons olive oil, vinegar, and salt and pepper to taste; puree. Set the sauce aside.
Cut the avocados into 1/2-inch chunks. Toss with the lemon juice and remaining 2 teaspoons olive oil.
Spread a scant tablespoon of the green sauce on each slice of bread. Arrange the avocado chunks on the bread, sprinkle with a pinch of ground pepper, and garnish with parsley. Serve immediately.