Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add the sausage with 1/2 cup water and cook, turning occasionally, until browned and cooked through, 15 to 20 minutes.
Meanwhile, preheat the broiler and lightly grease a 9-inch pie pan with olive oil. In a medium saucepan, combine the milk, 2 cups water, 1/2 tablespoon olive oil and 1 teaspoon salt and bring to a boil. Reduce the heat to low and slowly stir in the polenta. Cook until thickened, stirring constantly, about 2 minutes. Spread the polenta evenly in the pie pan. Top with the cheese and broil until golden, about 8 minutes.
In a medium skillet, heat the remaining 1 tablespoon olive oil over medium-high heat and add the garlic. Cook until the garlic is golden, 1 to 2 minutes. Add the broccoli, red pepper flakes and 1/4 cup water, cover and cook, stirring once, until the broccoli is fork-tender, about 5 minutes. Season to taste with salt.
Slice the sausage on the diagonal into 1/4-inch pieces and toss with the broccoli. Cut the polenta pie into wedges and top with the sausage and broccoli.