Coarsely rated goat's-milk gouda cheese or goat's-milk
Heat 2 tablespoons oil in large deep skillet over medium heat. Add onions; sauté until tender, about 10 minutes. Add garlic; stir 1 minute. Add lamb; cook until browned, breaking into pieces, about 15 minutes. Add cocoa and next 4 ingredients; stir 3 minutes. Stir in 4 cups broth and next 6 ingredients. Bring to boil; reduce heat to medium-low. Simmer uncovered until thickened, stirring often, about 1 hour. Spoon fat from top of chili. Season with salt and pepper. Thin with broth by 1/3 cupfuls. Stir in 2 tablespoons parsley.
Meanwhile, cook spaghetti in pot of boiling salted water until tender but still firm to bite, stirring occasionally. Drain. Transfer to large bowl. Toss with beans and 2 tablespoons oil. Season with salt and pepper.
Divide spaghetti among bowls. Top with chili. Garnish with cheese, onions, and parsley.