The creation of a spatially extended stable DC complex plasma crystal is a big experimental challenge and a topical area of research in the field of dusty plasmas. In this paper we describe a newly built and commissioned dusty plasma experimental device, DPEx-II, at the Institute for Plasma Research. The device can support the formation of large sized Coulomb crystals in a DC glow discharge plasma. The plasma in this L-shaped table-top glass chamber is produced between a circular anode and a long tray shaped cathode. It is characterized with the help of various electrostatic probes over a range of discharge conditions. The dust particles are introduced by a dust dispenser to form a strongly coupled Coulomb crystal in the cathode sheath region. The unique asymmetric electrode configuration minimizes the heating of dust particles and facilitates the formation of crystalline structures with a maximum achievable dimension of 40~cm X 15~cm using this device. A larger crystal has numerous advantages over smaller ones, such as higher structural homogeneity, fewer defects, lower statistical errors due to finite size effects etc.. A host of diagnostics tools are provided to characterize the Coulomb crystal. Results of a few initial experiments aimed at demonstrating the technical capabilities of the device and its potential for future dusty plasma research, are reported.