What part of the brain affects cognition

The brain changes as a function of experience and potential damage in a process known as plasticity.
The brain can generate new neurons through neurogenesis.
The motor cortex controls voluntary movements.
Body parts requiring the most control and dexterity take up the most space in the motor cortex.

The brain is a complex organ that is responsible for cognitive function.
How it does this is complicated, as there are many different layers to each part of the brain, each of which is responsible for performing certain functions.
Here is a look, from big to small, on how the brain functions:

The cerebrum is considered to be the main portion of the brain regulating thought, but this is further subdivided into more sections.
The cerebrum has three main sections, the left and right hemisphere and the corpus callosum between them.