Is the structure of crystalized white dwarf related to nuclear pasta? There is news of an analysis of a large number of nearby white dwarfs revealing a "pile-up" at a certain point in their cooling which has been predicted to happen due to a phase change where nuclear material crystalizes. This is analogous to a mixture of ice and water remaining at 0C while it is in the process of freezing (or thawing).

What is this crystalline material like? Is it really a lattice of Carbon and Oxygen nuclei in some recognizable structure (cubic BCC... etc.)? Is it related in some way to nuclear pasta?

Nature: Core crystallization and pile-up in the cooling sequence of evolving white dwarfs
It's thought to be crystalline in the same sense that diamonds are a crystal. The coulomb interactions between the positively charged ions becomes much larger than their thermal energies and they settle into a crystal lattice.

This both releases latent heat and increases the thermal heat capacity of the ions (roughly doubles it). This causes a "pile up" of white dwarfs with interior temperatures at around the crystallisation phase transition. However, the pile-up is not too steep because the freezing temperature increases with density and white dwarf interiors are roughly isothermal. This means they freeze from the inside out.

The crystalline structure is expected to be bcc.

I think the only thing this has in common with nuclear pasta is that they are both phase transitions. Nuclear pasta is the aggregation of nucleons (neutrons and protons) into wacky shapes in order to minimise the total energy density of the gas. The temperature is not really an issue here and it is all to do with density.