Quasi-phase-matching (QPM) has become one of the most common approaches for increasing the efficiency of nonlinear three-wave mixing processes in integrated photonic circuits. Here, we provide a study of dispersion engineering of QPM second-harmonic (SH) generation in stoichiometric silicon nitride (${\mathrm{Si}}_3{\mathrm{N}}_4$) waveguides. We apply waveguide design and lithographic control in combination with the all-optical poling technique to study the QPM properties and shape the waveguide dispersion for broadband spectral conversion efficiency inside ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides. By meeting the requirements for maximal bandwidth of the conversion efficiency spectrum, we demonstrate that group-velocity matching of the pump and SH is simultaneously satisfied, resulting in efficient SH generation from ultrashort optical pulses. The latter is employed for retrieving a carrier-envelope-offset frequency of a frequency comb by using an $f-2f$ interferometric technique, where supercontinuum and SH of a femtosecond pulse are generated in ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguides. Finally, we show that the waveguide dispersion determines the QPM wavelength variation magnitude and sign due to the thermo-optic effect.