Using long serrated knife, cut bottom crust and short ends off bread into 1" cubes (about 10 cups,loosely packed). Place cubes in large bowl. Add oil, thyme, and garlic; toss to coat. Spread cubes out on a large rimmed baking sheet. Sprinkle with salt and pepper. Bake until golden and slightly crunchy, stirring occasionally, about 20 minutes. Return cubes to same large bowl.
Melt butter in large skillet over medium-high heat. Add onion, celery, and bell pepper. Saute until vegetables are soft, about 10 minutes, add parsley.
Preheat oven to 375 degrees. Butter 11x7" glass baking dish. Stir vegetable mixture into bread cubes. Gradually add hot broth, tossing to coat evenly. Season stuffing to taste with salt and pepper and transfer to prepared dish. Cover dish with buttered foil, buttered side down. Bake stuffing until heated through, about 25 minutes. Uncover and bake until top is brown, about 25 minutes longer, and serve.