Preheat the oven to 350?F. Grease a 9 x 13-inch baking dish with 1 tablespoon olive oil.
Bring a medium pot of water to a boil. Add the spinach and cook until just wilted, about 30 seconds. Drain and rinse with cold water. Once cool, squeeze as much water as possible from the spinach, then coarsely chop and reserve; you should have about 3 cups.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the onions and cook until golden brown and tender, about 5 minutes. Add the garlic, 2 teaspoons of Italian Essence, 1/2 teaspoon salt, and 1/4 teaspoon black pepper and cook, stirring, until the garlic is fragrant, about 30 seconds. Add the artichokes and cook, stirring, another 2 minutes. Remove from the heat and reserve.
Combine the eggs, cream, milk, lemon juice, remaining 1 tablespoon Italian Essence, remaining 2 teaspoons salt, and remaining 1 teaspoon pepper in a large bowl. Whisk to combine. Add the bread cubes, spinach, artichoke mixture, Brie, 1/4 cup Parmesan, and parsley and stir to combine. If the bread does not absorb all of the liquid immediately, then let rest until it does, about 20 minutes.
Pour the bread pudding mixture into the prepared dish, sprinkle the remaining 1/4 cup Parmesan over the top, and drizzle with the remaining 2 tablespoons olive oil. Bake until firm in the center and golden brown, about 1 hour. Serve warm.
Makes 10 to 12 servings