We introduce the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design and science program. This haloscope plans to search for bosonic dark matter across the [10^{-3},1] eV ([0.24, 240] THz) mass range. BREAD proposes a cylindrical metal barrel to convert dark matter into photons, which a novel parabolic reflector design focuses onto a photosensor. This unique geometry enables enclosure in standard cryostats and high-field solenoids, overcoming limitations of current dish antennas. A pilot 0.7 m^{2} barrel experiment planned at Fermilab is projected to surpass existing dark photon coupling constraints by over a decade with one-day runtime. Axion sensitivity requires <10^{-20} W/sqrt[Hz] sensor noise equivalent power with a 10 T solenoid and 10 m^{2} barrel. We project BREAD sensitivity for various sensor technologies and discuss future prospects.