Crunchy Eggs with Piquillo Peppers

Preparation Line a rimmed baking sheet with plastic wrap. Pour water into a large skillet to a depth of 2". Bring water to a boil; lower heat to maintain a simmer. Add vinegar. Break 1 egg into a small ramekin or bowl. Partially immerse cup in water and quickly slide egg into water. Repeat with remaining 3 eggs. Cook until whites are firm but yolks are still runny, about 3 minutes. Using a slotted spoon, transfer eggs to prepared sheet. Trim eggs' ragged edges with a knife. Slide eggs into a medium bowl filled with ice water. Cover bowl; chill until cold.DO AHEAD: Can be made 1 day ahead. Keep chilled. Heat extra-virgin olive oil in a medium heavy skillet over medium heat. Add garlic; sauté for 1 minute. Add ham; sauté for 1 minute. Add peppers, Sherry, and marjoram; simmer until almost all liquid evaporates, about 10 minutes. Season with salt and pepper. Remove from heat. Using a slotted spoon, transfer eggs to a kitchen towel to drain. Mix panko, thyme, and 1 teaspoon salt in a medium bowl. Place egg whites in another medium bowl; whisk to loosen. Gently roll 1 poached egg in egg whites, then in panko mixture (some bare spots may remain). Place on plate. Repeat with remaining eggs, egg whites, and panko. Heat 3/4 cup olive oil in a medium heavy skillet over medium heat. Gently slide eggs, one at a time, into oil; cook until crumbs begin to brown, about 2 minutes per side. Using slotted spoon, transfer eggs to paper towels to drain. Sprinkle lightly with salt. Divide pepper mixture among 4 plates. Top each with 1 egg and serve.

Preparation Line a rimmed baking sheet with plastic wrap. Pour water into a large skillet to a depth of 2". Bring water to a boil; lower heat to maintain a simmer. Add vinegar. Break 1 egg into a small ramekin or bowl. Partially immerse cup in water and quickly slide egg into water. Repeat with remaining 3 eggs. Cook until whites are firm but yolks are still runny, about 3 minutes. Using a slotted spoon, transfer eggs to prepared sheet. Trim eggs' ragged edges with a knife. Slide eggs into a medium bowl filled with ice water. Cover bowl; chill until cold.DO AHEAD: Can be made 1 day ahead. Keep chilled. Heat extra-virgin olive oil in a medium heavy skillet over medium heat. Add garlic; sauté for 1 minute. Add ham; sauté for 1 minute. Add peppers, Sherry, and marjoram; simmer until almost all liquid evaporates, about 10 minutes. Season with salt and pepper. Remove from heat. Using a slotted spoon, transfer eggs to a kitchen towel to drain. Mix panko, thyme, and 1 teaspoon salt in a medium bowl. Place egg whites in another medium bowl; whisk to loosen. Gently roll 1 poached egg in egg whites, then in panko mixture (some bare spots may remain). Place on plate. Repeat with remaining eggs, egg whites, and panko. Heat 3/4 cup olive oil in a medium heavy skillet over medium heat. Gently slide eggs, one at a time, into oil; cook until crumbs begin to brown, about 2 minutes per side. Using slotted spoon, transfer eggs to paper towels to drain. Sprinkle lightly with salt. Divide pepper mixture among 4 plates. Top each with 1 egg and serve.