Broadening Opportunities Through Education Act - Directs the Secretary of Education to award competitive grants to states that make school attendance compulsory through age 17.

Requires states to use their grant to improve their secondary school programs, such as by:

• establishing or expanding work-based programs that integrate academic and career-based skills;
• implementing an early warning system that helps high schools and their feeder middle schools identify and assist struggling students;
• establishing grade and school transition programs and supports;
• personalizing the school experience and increasing student engagement through service-learning and experiential, work-based, and other learning opportunities;
• providing extended-learning opportunities by the school day, week, or year; and
• increasing student supports through activities such as student advisories, counseling, and one-to-one mentoring.