We present photometric and spectroscopic observations of the 03fg-like type Ia supernova (SN Ia) ASASSN-15hy from the ultraviolet (UV) to the near-infrared (NIR). ASASSN-15hy shares many of the hallmark characteristics of 03fg-like SNe Ia, previously referred to as "super-Chandrasekhar" SNe Ia. It is bright in the UV and NIR, lacks a clear i-band secondary maximum, shows a strong and persistent C II feature, and has a low Si II \(\lambda\)6355 velocity. However, some of its properties are also extreme among the subgroup. ASASSN-15hy is under-luminous (M\(_{B,peak}=-19.14^{+0.11}_{-0.16}\) mag), red (\((B-V)_{Bmax}=0.18^{+0.01}_{-0.03}\) mag), yet slowly declining (\(\Delta{m_{15}}(B)=0.72 \pm 0.04\) mag). It has the most delayed onset of the i-band maximum of any 03fg-like SN. ASASSN-15hy lacks the prominent H-band break emission feature that is typically present during the first month past maximum in normal SNe Ia. Such events may be a potential problem for high-redshift SN Ia cosmology. ASASSN-15hy may be explained in the context of an explosion of a degenerate core inside a non-degenerate envelope. The explosion impacting the non-degenerate envelope with a large mass provides additional luminosity and low ejecta velocities. An initial deflagration burning phase is critical in reproducing the low \(^{56}\)Ni mass and luminosity, while the large core mass is essential in providing the large diffusion time scales required to produce the broad light curves. The model consists of a rapidly rotating 1.47 \(M_{\odot}\) degenerate core and a 0.8 \(M_{\odot}\) non-degenerate envelope. This "deflagration core-degenerate" scenario may result from the merger between a white dwarf and the degenerate core of an asymptotic giant branch star.