"""Extracts all boxed expressions from a given text.

This function searches for all occurrences of the pattern `\boxed{...}` in the input text and extracts the content within the braces. It handles nested boxed expressions by tracking the depth of the braces.

Args:
    text (str): The input text containing zero or more `\boxed{...}` patterns.

Returns:
    List[str]: A list of strings, each representing the content extracted from a `\boxed{...}` pattern. If no patterns are found, an empty list is returned.

Note:
    - The function correctly handles nested boxed expressions by counting the depth of the braces.
    - The search is case-sensitive and assumes the exact pattern `\boxed{...}`.
"""
You should write code starting with:
from typing import List

def extract_boxed(text: str) -> List[str]:
    pass

