In this paper, we demonstrate a pulse energy-governed nonlinear self-switching of femtosecond pulses at wavelength of 1700 nm in a highly nonlinear high index contrast dual-core fibre. The fibre structure is composed of two microdimension cores and a solid cladding made of two thermally matched soft glasses developed in-house. A double switching behaviour under monotonic increase of the input pulse energy from 1 nJ to 3 nJ was observed at 35 mm fibre length in its anomalous dispersion region. A spatial intensity distribution measurement identified a switching contrast of 16.7 dB, and the registered spectra of the two output channels revealed a broadband switching behaviour within 150 nm. The obtained results indicate a novel type of solitonic switching and represent a significant progress in comparison to the previous experimental works and has a high application potential.