Heat 1 cup oil in a small saucepan over medium-high heat. Deep fry the eggs in the hot oil until they are golden brown, 5 to 7 minutes; set aside.

Combine the chile peppers, garlic, shallots, tomatoes, and shrimp paste in a food processor; blend into a paste. Add in peanut oil. Process again until smooth.

Heat 1 tablespoon oil in a large skillet over medium heat. Pour the chile pepper mixture into the skillet. Stir the vinegar, sugar, salt, and pepper into the mixture. Add the fried eggs to the mixture, turning to coat. Reduce heat to medium-low; simmer until fragrant, about 5 minutes.