Heat 2 tablespoons olive oil in a large nonstick skillet over medium heat. Add the andouille and cook until lightly browned, about 3 minutes. Add the bell pepper and celery, toss to coat and cook until softened, 3 to 4 minutes. Stir in the scallions, garlic and Cajun seasoning and cook until slightly softened, about 30 seconds. Pour in the tomatoes and 1/4 cup water; season with 1/2 teaspoon salt and a few grinds of pepper. Bring to a simmer and cook until slightly thickened, 8 to 10 minutes.
Meanwhile, preheat the broiler. Brush the polenta slices on both sides with the remaining 1 tablespoon olive oil; arrange on a baking sheet. Broil until crisp around the edges, 10 to 12 minutes.
Using the back of a spoon, make 8 spaces in the tomato sauce for the eggs. Crack in the eggs, cover and cook until the whites are set but the yolks are still runny, 6 to 8 minutes. Top with the parsley, celery leaves and more Cajun seasoning. Serve with the polenta.