Crispy Caper Chicken Sandwich with Homemade Mayonnaise Recipe

Name: Crispy Caper Chicken Sandwich with Homemade Mayonnaise Recipe
Ingredients: For the Chicken; 3 slices white sandwich bread, torn into pieces; 2 tablespoons unsalted butter, cut into small pieces and chilled; 1 tablespoon finely grated lemon zest; 1 small garlic clove, minced; 6 tablespoons nonpareil capers, drained; Salt and pepper; 1/3 cup all-purpose flour; 2 large eggs, at room temperature; 4 thin-cut chicken cutlets; 3/4 cup olive oil; For the Mayonnaise; 1 large egg yolk, at room temperature; 2 teaspoons Dijon mustard; 2 teaspoons lemon juice; 2/3 cup vegetable oil; For the Assembly; 4 sturdy rolls, split in half; 2 tablespoons unsalted butter, softened