How to modify Jetty Client Request after TLS handshake is complete?

JettyClient.java

// Jetty version: 12.0.6
public class JettyClient {
    public static void main(String[] args) throws Exception {
        SecurityProviders.init(); // initializes the Conscrypt and BouncyCastle security providers

        SslContextFactory.Client sslContextFactory = new SslContextFactory.Client();
        // This disables SSL certificate validation
        // handy for localhost testing, not so handy in production
        sslContextFactory.setTrustAll(true);

        SigAuthClientListener sigAuthClientListener = new SigAuthClientListener();

        ClientConnector clientConnector = new ClientConnector();
        clientConnector.setSslContextFactory(sslContextFactory);
        // clientConnector.setConnectBlocking(true); // this doesn't change anything

        HttpClient client = new HttpClient(new HttpClientTransportDynamic(clientConnector));

        client.addBean(sigAuthClientListener);
        client.start();
        String host = "127.0.0.1";
        int port = 8090;

        String url = String.format("https://%s:%d/ping", host, port);
        Request request = client.newRequest(url).listener(sigAuthClientListener);
        ContentResponse res = request.send();
        System.out.println("Got response: " + res.getStatus() + " " + res.getReason());
        System.out.println(res.getContentAsString());
        client.stop();
    }
}

SigAuthClientListener.java

// Jetty version: 12.0.6

public class SigAuthClientListener implements Connection.Listener, Request.Listener, SslHandshakeListener {
    @Override
    public void onOpened(Connection connection) {
        System.out.println("Connection opened");
    }

    @Override
    public void onBegin(Request request) {
        System.out.println("Request begin");
        // This is my last chance to modify the request headers,
        // but the TLS handshake hasn't completed yet!
    }

    @Override
    public void handshakeSucceeded(Event event) throws SSLException {
        System.out.println("Handshake succeeded");
    }

    @Override
    public void onCommit(Request request) {
        System.out.println("Request commit");
        // This happens after the handshake
        // but we cannot modify the headers here, they have already been serialized
        //        :(
    }
}

/*
Output:

Connection opened
Request begin
Handshake succeeded
Request commit
*/