Preheat oven to 400°F, Lightly butter a 9x13-inch glass baking dish; set aside.
Tear or cut bread into 1-inch pieces. Place bread pieces in a large mixing bowl; set aside.
In a large skillet, melt the butter over medium-high heat. Add the butternut squash and parsnips. Add 1 teaspoon salt and 1 teaspoon pepper. Cook, stirring occasionally, for 5 minutes or until slightly softened. Set aside to cool.
Drizzle the olive oil over the bread pieces, and toss gently. Add the brown sugar, cinnamon, 2 teaspoons salt, 1 teaspoon pepper, and chopped thyme leaves. Toss the ingredients together until the bread pieces are well coated.
In another bowl whisk together the heavy cream, eggs, and brandy. Pour the cream mixture over the bread mixture. Add the cooled vegetables, and toss gently until the bread is well coated with the custard mixture (but the bread still reamins in chunks).
Spoon the mixture into the buttered baking pan. Bake for 40 to 45 minutes, or until the bread pudding is puffed and golden.