You are restricted to the AT commands available though and that might restrict what you want to achieve.
You need to give more details around the sensor and what data you want to communicate.
For example, you may want to put firmware on the ESP module that receives packets of data from the microcontroller and then sends them on via MQTT.
Is there something specific on the Texas board you need? Have you considered using a better esp8266 module (ESP-12 / NodeMCU/Wemos) or even an ESP32 as a simpler all in one solution?