string path = "file.txt";
File.WriteAllText(path, File.ReadAllText(path, Encoding.UTF8), Encoding.BigEndianUnicode);

using (var srcReader = new StreamReader("input.txt", Encoding.UTF8))
using (var dstStream = File.Create("output.txt"))
{
    byte[] preamble = Encoding.BigEndianUnicode.GetPreamble();
    dstStream.Write(preamble, 0, preamble.Length);
    
    var encoder = Encoding.BigEndianUnicode.GetEncoder();

    const int BLOCK_SIZE = 1000;
    char[] chars = new char[BLOCK_SIZE];
    byte[] tempBuf = new byte[chars.Length*2];
    while(true)
    {
        int charsRead = srcReader.ReadBlock(chars, 0, chars.Length);
        if (charsRead == 0) break;
        
        int byteCount = encoder.GetByteCount(chars, 0, charsRead, true);
        if (byteCount > tempBuf.Length) Array.Resize(ref tempBuf, byteCount);
        
        int charsUsed, bytesUsed; bool completed;
        encoder.Convert(chars, 0, charsRead, tempBuf, 0, tempBuf.Length, true, out charsUsed, out bytesUsed, out completed);
        Debug.Assert(completed);
        
        dstStream.Write(tempBuf, 0, byteCount);
    }
}