Dual-comb spectroscopy is emerging as a powerful technique for broad spectral bandwidth spectroscopy of molecules. Time-domain interference phenomena induced by two frequency combs of slightly different line spacing are utilized. In the frequency domain, each pair of optical lines, one from each comb, produces a radio-frequency beat note on the detector. Such beat signals form a comb in the radio-frequency region, with lines spaced by the difference in line spacing of the two optical combs. Optical frequencies are thus converted into radio-frequencies. Most of the time, the implementation of dual-comb systems has relied on mode-locked lasers and the realization of phase-coherence between the two combs is then very complex. In this situation, we demonstrate a new scheme of broadband dual-comb spectroscopy based on continuous-wave lasers and cascaded electro-optic modulators. From the same continuous-wave seed laser, we generate two mutually-phase-coherent optical frequency combs of different line spacing. A combination of intensity and phase electro-optic modulators is exploited to produce flat-top comb spectra. We will demonstrate that this system becomes a viable platform for environmental gas monitoring.