Thanks for your input, however I can replicate the problem using a client based on Mojo::IOLoop, like this for example:

use warnings;
use strict;

use IO::Socket::SSL 'SSL_VERIFY_NONE';
use Mojo::IOLoop;

use Time::HiRes qw'time';

use constant {
  BUFSIZE => 16384,
  INTERVAL => 1,
};

my $PEER_ADDR='192.168.1.10';
my $PEER_PORT=1234;

my $transferred=0;
my ($currentTime,$intvlStart,$intvlEnd);

Mojo::IOLoop->client(
  { address => $PEER_ADDR,
    port => $PEER_PORT,
    tls => 1,
    tls_options => {SSL_verify_mode => SSL_VERIFY_NONE},
    tls_verify => SSL_VERIFY_NONE },
  sub {
    my ($loop, $err, $stream) = @_;
    if(defined $err) {
      print "Failed to connect to SSL server: $err\n";
      return;
    }
    print "Connected, downloading data from server...\n";
    $currentTime=time();
    ($intvlStart,$intvlEnd)=($currentTime,$currentTime+INTERVAL);
    $stream->on(close => sub {die "Connection closed by peer"});
    $stream->on(error => sub {
      die "Failed to read from SSL socket: $_[1]"
    });
    $stream->on(read => sub {
      my ($stream,$readData)=@_;
      my $readLength=length($readData);
      die "Unexpected read length: $readLength"
        unless($readLength == BUFSIZE);
      $transferred+=BUFSIZE;
      $currentTime=time();
      if($currentTime >= $intvlEnd) {
        printReport();
        initNewInterval();
      }
    });
  });

sub printReport {
  my $speed=formatSize($transferred/($currentTime-$intvlStart));
  print "Transfer speed: $speed/s\n";
}

sub formatSize {
  my $size=shift;
  my @UNITS=('',qw'K M G T');
  my $unitIdx=0;
  while($size >= 1000 && $unitIdx < $#UNITS) {
    $size/=1000;
    $unitIdx++;
  }
  $size=sprintf('%.2f',$size) if(index($size,'.') != -1);
  return $size.' '.$UNITS[$unitIdx].'B';
}

sub initNewInterval {
  $transferred=0;
  $intvlStart=$currentTime;
  $intvlEnd+=INTERVAL while($intvlEnd < $intvlStart+INTERVAL/2);
}

print "Connecting to SSL server ($PEER_ADDR:$PEER_PORT)\n";
Mojo::IOLoop->start();
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When I perform the test using this Mojo-based non-blocking SSL client, I have a CPU core which is used at 100% (~40% us, ~10% sy, ~50% si), exactly like with my "low-level" non-blocking SSL client implementation. The problem is that when I use this Mojo-based client, I don't have access to the number of sysread calls which failed due to SSL_WANT_READ, so I have less information to provide for debugging.

For the record, if I use a blocking SSL client (still in Perl) instead, the highest CPU core usage for a 1Gbps transfer is at 55% on this system...