Here is the answer combining HttpClient with HttpRequestMessage.
HttpRequestMessage, which stores data and the client that processes data sending.
WebRequestHandler handler = new WebRequestHandler();
X509Certificate2 certificate = GetMyX509Certificate();
handler.ClientCertificates.Add(certificate);
HttpClient client = new HttpClient(handler);
var request = new HttpRequestMessage (HttpMethod.Get, "myapi/?myParm=" + aParm);
HttpResponseMessage response = await client.SendAsync (request);
response.EnsureSuccessStatusCode();
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