Trouble with SSL using ESP-01 and api.telegram.org

My project is based on a custom "bare-bone" style Arduino and based on an ATMEGA1284. The custom board doesn't support simply plugging in a shield. I am therefore trying to use an ESP-01 module and the (excellent!) WiFiEsp library.

It is simply not possible to connect to api.telegram.org. Even the sample "WebClientSSL" which comes with the WiFiESP library, which works fine for Google, won't work for api.telegram.org

After much debugging, I have tracked the problem to the establishing of the connection itself. I have duplicated the problem completely without any Arduino code by typing the commands manually into SerialMonitor with an ESP-01 module plugged into a USB adapter.

When issuing AT+CIPSTART=3,"SSL","www.google.com",443 I almost immediately receive 3,CONNECT followed by OK.

When issuing AT+CIPSTART=3,"SSL","api.telegram.org",443 I almost immediately receive 3,CLOSED followed by OK. (Immediate = about 40 milliseconds according to the SerialMonitor timestamps)

Subsequent AT+CIPSEND works fine on Google but receives some "link is not valid" message for api.telegram.org, presumably because the connection was not properly established.

I have no idea if the ESP-01 has chosen to close the connection for some reason or if api.telegram.org closed (or refused) the connection.

I don't think the problem is with the ESP-01 or firmware. I have several modules with various firmware (the latest is 1.5) and they all behave identical. I really don't want to reflash the module which is why I haven't moved to the WiFiEspAT library (though I am enviously eyeing some of the additional functionality it provides!).

If anyone has an idea why the connection doesn't go through, I would be most grateful. I would also greatly appreciate any tips anyone may have as to how I could investigate the problem further. So far, telegram support hasn't answered my inquiry.