The part of the brain whose anatomy is most similar to the spinal cord is the

Brainstem.

The brainstem is the portion of the central nervous system that's located between the spinal cord and the diencephalon and it occupies the posterior cranial fossa in front of the cerebellum. It is divided into three parts: the rachidian bulb, the pons, and the midbrain.
It's in the brainstem that can be found the commanding nucleus of the most basic homeostatic mechanisms such as heart rate, breathing, and nociception.