We present the confirmation of two new planets transiting the nearby mid-M dwarf LTT 3780 (TIC 36724087, TOI-732, V = 13.07, Ks = 8.204, Rs = 0.374 R⊙, Ms = 0.401 M⊙, d = 22 pc). The two planet candidates are identified in a single Transiting Exoplanet Survey Satellite sector and validated with reconnaissance spectroscopy, ground-based photometric follow-up, and high-resolution imaging. With measured orbital periods of Pb = 0.77, Pc = 12.25 days and sizes rp,b = 1.33 ± 0.07, rp,c = 2.30 ± 0.16 R⊕, the two planets span the radius valley in period–radius space around low-mass stars, thus making the system a laboratory to test competing theories of the emergence of the radius valley in that stellar mass regime. By combining 63 precise radial velocity measurements from the High Accuracy Radial velocity Planet Searcher (HARPS) and HARPS-N, we measure planet masses of and M⊕, which indicates that LTT 3780b has a bulk composition consistent with being Earth-like, while LTT 3780c likely hosts an extended H/He envelope. We show that the recovered planetary masses are consistent with predictions from both photoevaporation and core-powered mass-loss models. The brightness and small size of LTT 3780, along with the measured planetary parameters, render LTT 3780b and c as accessible targets for atmospheric characterization of planets within the same planetary system and spanning the radius valley.