Heat 1 Tbsp. oil in a Dutch oven or heavy cast iron skillet over medium heat. Saute half the garlic cloves until beginning to turn golden brown, 1–2 minutes. Add spinach to pot. Toss to coat; season with salt and pepper. Cook until spinach is wilted but still bright green, 2–3 minutes. Transfer to a medium bowl; set aside. Wipe out pot.

Heat 2 Tbsp. oil in same pot over medium heat. Add onion and the remaining garlic cloves. Cook, stirring often, until onion is softened, 3–4 minutes. Add cumin and paprika. Saute until fragrant, 1–2 minutes. Add chickpeas and tomatoes. Cook, stirring occasionally, until tomatoes start to caramelize and chickpeas begin to brown, 8–10 minutes.

Add 3 cups of broth and bring to a simmer, scraping up any browned bits from bottom of pan. Reduce heat to medium, and simmer, occasionally mashing some chickpeas with the back of a spoon or a potato masher, until sauce is thickened, 15–20 minutes. Fold in spinach and simmer for flavors to meld, adding more broth by 1/4-cupfuls if too thick, 8–10 minutes.

Pour oil into a large heavy skillet to a depth of 1/8" (about 1/4 cup) and set it over high heat. Follow these directions to fry the eggs, two at a time, depending on the size of your pan. Transfer to a plate and repeat with remaining 2 eggs.

Spoon chickpea stew into bowls and top each with a fried egg. Serve with crusty bread and a good Spanish wine, white or red.