The central meridian on that picture looks like it's around 10E which does allow the Chukchi peninsula to stay connected to the rest of Asia.
What do you want to do with the map? Plate Carree is simple and rectangular, but it doesn't preserve any properties. You might look at Goode's Homolosine (land-based option still preserve Chuckchi too) or Mollweide, or Robinson.
Melita