Slowly whisk in the wine, then the half-and-half, a splash at a time so no lumps form. Simmer gently for 3-4 minutes, whisking often, until the sauce coats the back of a spoon.
Take the pan off the heat. Stir in the cheddar, Monterey Jack, and 2 tablespoons Parmesan until smooth. Add paprika, cayenne, Worcestershire, lemon juice, and salt, then taste.