Among the insect species reared as alternative protein sources, Hermetia illucens (black soldier Fly, BSF) has shown a huge potential mostly due to its high protein content, its bioconversion rates, and versatility in using different feeding substrates. Insect rearing may use continuous or batch feeding regimes and, among the used substrates, supermarket feedstock waste has gained recent interest under a circular economy perspective, but several uncertainties remain regarding the heterogeneity and the potential effects of the quantity and quality of these substrates on BSF larvae (BSFL) development. In this experimental work, five replicates of a hundred BSFL were fed in a continuous feeding regime, using seven different isolated vegetables as substrates (wheat bran, pumpkin, apple, grape pomace, red onion, red cabbage, and spinach), at three different temperatures (20, 25, and 30 °C) and two substrate moisture conditions (natural and 70% substrate moisture), until 50% of the larvae achieved the prepupal stage. BSFL performance and bioconversion parameters were evaluated. Our results show that some substrates should be avoided when rearing Hermetia illucens on feedstocks. Among these, apple feed led to poorer and slower development performances with more than 100 days of larval stage, while grape pomace and spinach showed higher mortality rates, which may be due to some anti-nutritional compounds. Larvae fed on pumpkin, red cabbage, and red onion presented good bioconversion results with higher values of efficiency of conversion of digested feed between 14.4 and 25. This work delivers relevant results for black soldier fly reared on a continuous feeding system using vegetable feedstock substrates and their potential trade-offs.