Simple GET request with ESP8266HTTPClient
As Musa said, I needed to suply the website certificate footprint to http.begin.

void loop() {
  HTTPClient http;
  String thumbprint="08:3B:71:72:02:43:6E:CA:ED:42:86:93:BA:7E:DF:81:C4:BC:62:30";
  String path = "https://calm-falls-41696.herokuapp.com/api/v1/cards.json";
  http.begin(path, thumbprint);
  int httpCode = http.GET();
  Serial.println(httpCode);
  if(httpCode == HTTP_CODE_OK) {
    Serial.print("HTTP response code ");
    Serial.println(httpCode);
    String response = http.getString();
    Serial.println(response);
 }
  http.end();
  delay(1000);
}