Preheat broiler. Heat 2 tablespoons oil in a large, heavy, ovenproof skillet over medium heat. Add 1 garlic clove, chiles, and bay leaf and cook, stirring constantly, just until fragrant, 1–2 minutes (do not allow garlic to burn). Add tomato; season with salt and pepper. Cook, stirring and smashing tomato with the back of a wooden spoon, until tomato is completely broken down, about 5 minutes.
Add tomato paste and cook, stirring constantly, until paste is deep red and caramelized, 3–4 minutes. Stir in beans and broth. Bring to a brisk simmer and cook until juices are slightly reduced and thickened, 3–4 minutes. Season to taste with salt and pepper.
Combine remaining 2 garlic cloves, 2 tablespoons oil, shrimp, and paprika in a medium bowl; season with salt and pepper and toss to evenly coat shrimp. Scatter shrimp over beans in an even layer.
Broil until shrimp are golden and cooked through, about 3 minutes. Drizzle remaining 2 tablespoons oil over shrimp and beans; garnish with parsley. Serve with bread, if desired.
Dried chiles de árbol are available at Latin markets, specialty foods stores, and some supermarkets.