"""Extract all top-level \boxed{...} contents from the input string, handling nested braces correctly.

This function scans the string manually to ensure proper brace matching, allowing for nested expressions inside \boxed{}, but only extracting the outermost matched segments.

Behavior:
- For nested boxed expressions like \boxed{\boxed{\boxed{42}}}, it returns ['\boxed{\boxed{42}}'] — treating the entire nested structure as one match.
- For multiple separate boxed expressions like \boxed{42} and \boxed{42}, it returns ['42', '42'].

Args:
    text (str): The input string containing \boxed{...} expressions.

Returns:
    list[str]: A list of strings extracted from each top-level \boxed{...} block.
"""
You should write code starting with:
from typing import List

def find_boxed_content_with_boxed(text: str) -> List[str]:
    # TODO: Implement this function based on the docstring.
    pass

