Caesar Salad French Laundry

Name: Caesar Salad French Laundry
Ingredients: ANCHOVY DRESSING (makes 2 cups); 1 1⁄2 tablespoons chopped garlic; 1 1⁄2 tablespoons chopped shallots; 1⁄4 cup balsamic vinegar; 2 tablespoons Dijon mustard; 1 teaspoon fresh lemon juice; 2 salt-packed anchovy fillets, deboned and soaked in milk,rinsed and drained (I used anchovy paste in the tube); 1 large egg yolk (I omitted and it emulsified wonderfully); 1 cup extra virgin olive oil; 1 cup canola oil; white pepper; CUSTARDS; 2⁄3 cup heavy cream; 2⁄3 cup milk; 3 1⁄2 ounces parmigiano-reggiano cheese, cut into 1/2 inch pieces; 2 large eggs; 1 large egg yolk; kosher salt; 3 cups chiffonade romaine lettuce (long narrow strips, cut from the heart or small inner leaves); 2 tablespoons freshly grated parmigiano-reggiano cheese; fresh ground black pepper; 12 croutons, from a baguette about 1/4 inches thick,toasted lightly; parmigiano-reggiano cheese, shavings for garnish (made with a vegetable peeler--should be VERY thin); FOR THE GLAZE; 2 cups balsamic vinegar