Worldwide, French beans (Phaseolus vulgaris L.), tomato (Solanum lycopersicum L.), and kales (Brassica oleracea L. var. acephala) are considered economically important food crops. There is a rapid decline in their yield due to severe soil degradation. Thus, high commercial fertilizer inputs are crucial, though they remain expensive and inaccessible to resource poor farmers. We investigated the comparative performance of composted black soldier fly frass fertilizer (BSFFF), conventionally composted brewer's spent grain (BSG), commercial organic fertilizer (Evergrow), and mineral [nitrogen, phosphorus, and potassium (NPK)] fertilizer on growth, yield, N use efficiency, and nutritional quality (crude protein, crude fiber, crude fats, ash, and carbohydrate concentrations) of tomatoes, kales, and French beans under greenhouse and open-field conditions for two seasons. The fertilizers were applied at rates equivalent to 371 kg of N ha−1. For each crop, the plots were treated with sole rates of BSFFF, BSG, Evergrow, and NPK to supply 100% of the N required. Additional treatments included a combination of BSFFF and NPK, and BSG and NPK so that each fertilizer supplies 50% of the N required. The control treatment consisted of unfertilized soil. Results show that vegetable yields achieved using a combination of BSFFF and NPK were 4.5, 2.4, and 5.4-folds higher than the yield from the control treatment for tomatoes, kales, and French beans, respectively. The combined application of BSFFF and NPK produced 22–135%, 20–27%, and 38–50% higher yields than sole NPK for tomatoes, kales, and French beans, respectively, under both greenhouse and open-field conditions. The highest agronomic N use efficiency was achieved in sole BSFFF-treated plots compared to sole BSG and Evergrow. The N taken up by the vegetables was significantly higher when BSFFF and NPK were integrated. Vegetables grown using a combination of BSFFF and NPK had the highest crude protein and ash concentrations. Our findings demonstrate that the integration of BSFFF and NPK in vegetable cropping systems at the recommended rate of 1.24 t ha−1 BSFFF and 322 kg ha−1 NPK would improve soil health, boost yield, and nutritional quality of vegetable crops.