Smoky Spanish Potatoes and Eggs

Name: Smoky Spanish Potatoes and Eggs
Ingredients: 3 Tbsp. plus 2 tsp. olive oil, divided; 1½ lbs. Yukon gold potatoes (about 3 medium), cut into 1-inch pieces; 1¾ tsp. kosher salt, divided; 1 medium onion, roughly chopped; 3 cloves garlic, roughly chopped; 2–3 chiles from a can of chiles in adobo, depending on your preferred spice level, roughly chopped, plus 2 Tbsp. sauce from the can; 1 medium tomato, roughly chopped; 1 Tbsp. tomato paste; ½ tsp. smoked paprika; ½ tsp. ground cumin; 2 Tbsp. sherry vinegar; Freshly ground black pepper; 3 large eggs; Chopped parsley and mayonnaise, for serving