Connecting Broadband Deserts Act of 2019 This bill requires the Federal Communications Commission (FCC) to conduct an annual inquiry on the availability of advanced telecommunications capability in broadband deserts, including whether such capability is being deployed in a reasonable and timely fashion. If it is not, the FCC shall take immediate action to accelerate deployment of such capability by removing barriers to infrastructure investment and promoting competition. The term "broadband desert" means a census block in an urban area in which fewer than 33% of end-user premises do not have access to advanced telecommunications capability.