A static inner class cannot access the (non-static) members of the containing class. But Node doesn't need to access these members - e.g. root. So Node could be static:

However, that means a static inner Node class has no access to the generic type parameters declared by the containing BST class.

So a static inner Node class must itself declare generic parameters:

public class BST<Key extends Comparable<Key>, Value>
{

  private Node<Key, Value> root;

  private static class Node<K, V>
  {
    private K key;
    private V val;
    private Node<K,> left;
    private Node<K,V> right;
  
    public Node(K k, V v)
    {
      key = k;
      val = v;
      left = right = null;
    }

    public Node()
    {
      this(null);
    }     
  }
}