Heat oven to 350 degrees F. In a large pot of boiling, salted water, cook broccoli until bright green, 3 minutes. Transfer to a bowl of ice water to cool, drain and set aside.
In a large skillet over medium-high heat, heat 2 tablespoons oil; cook onion and garlic, stirring often, until soft, about 4 minutes. Add merguez or sausage and cook, breaking up with a wooden spoon, until browned and crisp, about 5 minutes more. Remove from heat.
Lightly oil a 2-quart baking dish. In a large bowl, toss bread with spinach, broccoli and sausage mixture, then transfer to prepared dish. In a small bowl, whisk eggs with milk or broth and feta; season with salt and freshly ground black pepper. Pour egg mixture over bread, pressing down gently to be sure that the bread absorbs the custard. Cover dish tightly with foil and bake 20 minutes. Uncover, and bake until golden brown on top, 10 to 15 minutes more. Let cool slightly before serving.