High-performance optical beam splitters are of fundamental importance for the development of advanced silicon photonics integrated circuits. However, due to the high refractive index contrast of silicon-on-insulator platforms, state-of-the-art nanophotonic splitters are hampered by trade-offs in bandwidth, polarization dependence and sensitivity to fabrication errors. Here, we present a new strategy that exploits modal engineering in slotted waveguides to overcome these limitations, enabling ultra-broadband polarization-insensitive optical power splitters with relaxed fabrication tolerances. The proposed splitter design relies on a single-mode slot waveguide that is gradually transformed into two strip waveguides by a symmetric taper, yielding equal power splitting. Based on this concept, we experimentally demonstrate -3 ± 0.5 dB polarization-independent transmission for an unprecedented 390 nm bandwidth (1260-1650 nm), even in the presence of waveguide width deviations as large as ±25 nm.