In this work, we address the NER problem by splitting it into two logical sub-tasks: (1) Span Detection which simply extracts entity mention spans irrespective of entity type; (2) Span Classification which classifies the spans into their entity types. Further, we formulate both sub-tasks as question-answering (QA) problems and produce two leaner models which can be optimized separately for each sub-task. Experiments with four cross-domain datasets demonstrate that this two-step approach is both effective and time efficient. Our system, SplitNER outperforms baselines on OntoNotes5.0, WNUT17 and a cybersecurity dataset and gives on-par performance on BioNLP13CG. In all cases, it achieves a significant reduction in training time compared to its QA baseline counterpart. The effectiveness of our system stems from fine-tuning the BERT model twice, separately for span detection and classification. The source code can be found at https://github.com/c3sr/split-ner.