Take an Integer and print it in a Different Base Recursively (c++)
1. Names/Magic numbers
What is the magic number 55 in your base converter function?
I suggest giving it a name.
2. Bounds / Magic numbers / validation
Also, what are the upper and lower bounds on which bases are allowed? Only 2-9 since you are comparing with 9? That should also be specified and checked when reading the input.
3. Code formatting / style
Your code has a lot of space (empty lines and unnecessarily many newlines).
Unless your school requires you to follow that particular style, I suggest reformatting it into a more readable style. You can for example paste it into this formatter to get a more concise and readable code.
https://codebeautify.org/cpp-formatter-beautifier
For example, this is the output of reformatting part of your code.
void BaseConverter(int num, int base) {
  if (num == 0) {
    cout &lt;&lt; &quot;&quot;;
  }

  if (num &gt;= base) {
    BaseConverter(num / base, base);

    if (num % base &gt; 9) {
      cout &lt;&lt; char(num % base + 55);
    } else {
      cout &lt;&lt; num % base;
    }
  } else {
    cout &lt;&lt; num % base;
  }
}

4. cout multiple inputs
You can chain inputs to cout so you don't need to do this
cout &lt;&lt; endl;
cout &lt;&lt; endl;

But rather
cout &lt;&lt; endl &lt;&lt; endl;
5. File reading
It doesn't seem that the requirements for the assignment are to read from a file. If that is correct, I think you should skip the file reading and read from cin or a similar terminal input instead.