Toast couscous in 1 tbsp. oil in a medium saucepan over medium heat, stirring occasionally, until mostly golden, 7 to 8 minutes (if using fregola, omit oil and toasting). Add 1/4 tsp. salt and 2 cups water (and fregola, if using); bring to a boil. Cover, reduce heat, and simmer until barely tender, 8 to 10 minutes. Drain.
Cook garlic in remaining 1/4 cup oil in a large frying pan over medium heat until softened but still pale, 2 to 3 minutes. Add escarole and cook until it begins to wilt, 2 to 3 minutes. Add couscous and stir to coat, then add broth and 1/2 tsp. pepper and cook 2 to 3 minutes more. Season with about 1/4 tsp. salt and pepper to taste and keep warm.
Fill saucepan used for couscous three-quarters full of water, add vinegar, and cook over high heat until bubbles barely break the surface. Reduce heat to medium-low. Crack eggs into water and give water a gentle stir to ensure eggs aren't sticking to pan. Cook 3 minutes for runny yolks. With a slotted spoon, transfer eggs to paper towels. Sprinkle with about 1/4 tsp. salt and pepper to taste.
Divide escarole mixture among 4 soup plates and set an egg on each. Drizzle with more oil and sprinkle with parmesan.
*Buy fregola sarda from markethallfoods.com or at gourmet grocery stores. Look for duck eggs at Asian and farmers' markets.
Note: Nutritional analysis is per serving.