Microchip has BLE modules (like BM78) that can be controlled over UART via MCU host. These modules also have an I²C input for sensors. Once the data is received from the I²C sensor, the BLE module sends the unprocessed data to a predefined destination and can be processed at the application level.
Microchip also has an RN4870 module, Bluetooth® Low Energy PICtail™ / PICtail™ Plus Daughter Board. Please see the "RN4870 Sensor Board Support Package". This document details how you can put a script on this module to be used for basic sensor functionalities. The same way command mode is accessed (over UART) to program the module, you can enter another mode (scripting mode) where a script can be saved into the RN4870 module and will run at startup.
Finally, we also have ATSAMB11 single-chip MCU and BLE radio solutions with general purpose I/O and analog capability.