Heat oil in a skillet over medium heat. Sauté onion in hot oil until translucent and tender, about 5 minutes. Add roasted peppers and garlic; sauté until fragrant, 1 to 2 minutes. Stir in tomato paste, chili powders, cumin, and paprika. Sauté until well combined, 1 to 2 minutes more.

Stir in tomatoes and water. Season with salt and pepper. Raise heat to medium-high and bring mixture to a boil. Immediately reduce heat to medium and cook for about 5 minutes.

Reduce heat to medium-low. Make a well in tomato mixture for each egg; pour 1 egg into each well. Cover; poach until whites are firm and yolks have thickened but are not hard, 2 1/2 to 5 minutes.