1. Use a mandolin or a very sharp slicing knife and a cutting board to slice both cabbages as thinly as possible. Discard any large tough cabbage ribs. You'll have 12 to 14 cups. Use a vegetable peeler to thinly shave the carrots into pieces about 2 inches long. Put the mayonnaise, half-and-half, vinegar, 1 teaspoon salt and paprika into a large bowl; mix well. Add the cabbages and carrots. Toss to coat the cabbage well with dressing. Taste and season with more salt if desired. Refrigerate at least 1 hour or up to 2 days. Serve very cold. Note: To save time and knife work, you can use store-bought shredded cabbage; just be sure to buy a brand that is very finely shredded for tender slaw. You'll need 30-36 ounces of shredded cabbage for the serving size.