Final answer:
The layer of the small intestine with villi and brush borders is the mucosa.
Step-by-step explanation:
The layer of the small intestine that has villi with brush borders is the mucosa. The mucosa is the innermost layer of the small intestine and is responsible for absorption. The mucosa contains small hairlike projections called villi, which greatly increase the surface area for absorption. The brush borders of the villi contain microvilli, which further increase the surface area and contain enzymes for digestion.