Build Effective Teachers Through Essential Reforms to Teacher Education Assistance for College and Higher Education Grants Act of 2019 or the BETTER TEACH Grants Act of 2019 This bill revises provisions related to the Teacher Education Assistance for College and Higher Education (TEACH) Grant Program. Specifically, the bill includes within the purview of the grant program certain teacher preparation programs that were formerly ineligible, and it increases award amounts for teacher candidates enrolled as undergraduate juniors or seniors. The bill also expands TEACH Grant eligibility to associate degree students as well as to applicants obtaining a graduate degree in early childhood education. The bill clarifies the requirement that a TEACH Grant be treated as a Stafford Loan subject to repayment by establishing designated time frames within which a recipient must serve as a teacher. Further, the bill allows for the continued eligibility of a grant recipient despite certain changes to school description, teacher duties, or high-need field status. In addition, the bill requires the Department of Education to collect and make publicly available certain student data such as the number of (1) TEACH Grants awarded to students at a participating institution, (2) TEACH Grant recipients who complete their program of study and begin employment as a teacher in the first academic year following completion, and (3) TEACH Grant recipients who fulfill the terms of their agreement to serve and those whose grants are converted into loans for failure to fulfill such terms.