We examine room temperature band-to-band tunneling in 2D InAs/3D GaSb heterostructures. Specifically, multi-subband, gate-controlled negative differential resistance is observed in InAs/AlSb/GaSb junctions. Due to spatial confinement in the 10 nm-thick InAs layer, tunneling contributions from two distinct subbands are observed as sharp steps in the current-voltage characteristics. It is shown that the relative position of the steps can be controlled via external gate bias. Additionally, the extracted separation in the subband energy agrees well with the calculated values. This is the first demonstration of a gate controlled tunneling diode with multiple subband contributions.