This recipe has been updated and may differ from what was originally published or broadcast.
Combine the Garlic Confit, vinegar, Parmigiano-Reggiano, salt, pepper, anchovies, egg yolk and 2 tablespoons water in a blender, then blend on medium speed until smooth. With the motor running, slowly add the oil in a thin stream until it has been incorporated and the vinaigrette is creamy.
Use immediately or transfer to an airtight container and refrigerate. The vinaigrette will keep for up to 3 days.
Heat a grill for cooking over medium-high heat.
Sprinkle escarole with salt and pepper. Put escarole cut-side down on grill and cook until grill marks form, about 1 minute. Remove from grill and cut into 1 1/2-inch pieces. Transfer to a serving platter and toss with Caesar vinaigrette to taste.
Place the garlic in a small saucepan and add enough oil to cover. Set the saucepan over low heat and cook until the garlic is soft and pale golden, 30 to 35 minutes. Let the garlic cool in the oil. Store garlic covered in the oil, adding more oil if necessary.