Eggs Benedict Toast

Name: Eggs Benedict Toast
Ingredients: 3 large egg yolks; 1 tablespoon cold water; 1 teaspoon cornstarch; 1 teaspoon Dijon mustard; 1 ½ tablespoons fresh lemon juice, divided; 1 teaspoon kosher salt, divided; 12 tablespoons unsalted butter (6 ounces), melted, plus 2 tablespoons cold unsalted butter, divided; ⅛ teaspoon cayenne pepper; Warm water, as needed; 4 cold large eggs; 4 (1/2-inch-thick) sourdough bread slices, toasted; 8 thin prosciutto or speck slices (about 4 ounces); 2 tablespoons roughly chopped fresh soft herbs (such as tarragon and chives); Freshly ground black pepper (optional)