Air carrier flight crew reported on departure the entire weather radar system was inoperative with weather along the route. The flight crew diverted and landed safety at the departure airport.

Narrative

Check pilot conducting OE (Operating Experience); First Officer was Pilot Flying. During climb out from ZZZ airport; I elected to turn on the weather radar as it had become dark and there were clouds building along our route and WSI had shown radar returns along our route in northern flight path pre departure. The radar failed to turn on; followed by a WXR FAIL message on the Captain side ND (Navigation Display). I double checked the settings on the Weather Radar Panel. All Weather Radar Mode Switches were set appropriately; however; there was no tilt control; nor any gain control (the Gain Uncalibrated lights remained illuminated no matter the gain position) from the Weather Radar Panel. Selected the WXR switch on the FO EFIS (Electronic Flight Instrument System) Control Panel and had the same WXR FAIL message. At this point; I transferred radio duties to the FO and contacted Dispatch and Maintenance Control via the Crew Phone. Spent a few minutes discussing the issue with Maintenance Control and we determined that the entire radar system was inoperative to include the predictive wind shear system. The dispatcher and I agreed that with the weather in the ZZZ1 airport area we needed a functioning weather radar. Dispatch advised they were going to discuss the issue with Maintenance Control and the Coordinators and would possibly have us land short of ZZZ1 and try to repair the radar before continuing the flight. Shortly thereafter; we received an ACARS advising of a return to ZZZ airport to swap aircraft. During this exchange; the FO and I noticed a mild burnt bread smell. I called back and discussed the smell with the #1 Flight Attendant to determine if we were smelling the ovens or not. After we turned the flight around; we smelled the odor again; and again; I discussed things with the flight attendants in more depth and we were able to determine the smell was not coming from the ovens or the forward galley. With this new information; the FO and I discussed the odor was possibly associated with the failed radar. I contacted Dispatch and Maintenance Control again to advise of the development. Maintenance Control wanted to give it a 10-15 minutes and see what happened as it was intermittent. Dispatch and I agreed as we were equally split between ZZZ airport and ZZZ2 airport and could divert to either if the situation worsened. I informed Dispatch that it was my intention to advise ATC and attempt to get back to ZZZ airport. We advised ZZZ Center and proceeded direct to ZZZ airport as fast as we safely could. After advising; we noticed the odor a few more times; again highly intermittent and only lasted a few seconds. As we were landing over weight; when we talked to ZZZ approach; we elected to land the runway closest to our gate (XXR/Gate X) and requested ARFF (Airport Rescue and Firefighting). Approach and landing were uneventful; ARFF met us after we cleared the runway and followed us into our gate.