Chef John's Face Pie
1 large egg 1 large onion, finely chopped 1 large russet potato, peeled and quartered 1 pinch cayenne pepper 1 pinch salt 1 pound ground beef 1 pound ground pork 1 tablespoon butter 1 tablespoon water 1 teaspoon dried thyme 1 teaspoon freshly ground black pepper 1 teaspoon kosher salt 2 drops red food coloring, or as needed 2 sticks unsalted butter, sliced, frozen 2 teaspoons distilled white vinegar 2 teaspoons kosher salt 3 cups all-purpose flour 4 cloves garlic, crushed 7 tablespoons ice cold water ¼ teaspoon freshly grated nutmeg ¼ teaspoon ground allspice ¼ teaspoon ground mustard ½ cup finely diced celery ½ grape ½ teaspoon dried sage ½ teaspoon ground cinnamon ½ teaspoon ground ginger ⅛ teaspoon ground cloves