[This paper is part of the Focused Collection on Instructional labs: Improving traditions and new directions.] We present the pedagogical design and implementation of "ESSENCe": Experimental problem solving using Staging, Scaffolding, Embedded information sources, iNstruments, and Collaboration. Research in experimental physics requires problem-solving skills that include designing investigations, developing instrumentation techniques, troubleshooting, planning data analysis, and evaluating experimental outcomes. Most of these skills can be taught at the undergraduate level but are unfortunately skipped in traditional cookbook-recipe style labs. Since many physics experiments require electronics, the ESSENCe pedagogy presented here has been developed in the context of undergraduate electronics laboratory courses. The goals of ESSENCe labs are to help students apply their theoretical knowledge of electronics to hands-on open-ended experiments, understand properties of physical systems and limitations of measurements, and to learn how to work with sophisticated instruments used in experimental research. ESSENCe emphasizes collaboration with peers and teaching assistants. This paper presents the results of ESSENCe implementation in a sophomore undergraduate analog electronics lab of 45--60 students over multiple years in a top-ranked technological university in India. A mixed methods study was conducted to analyze students' development of experimental problem-solving skills through repeated measures of performance on experimental tests and video analysis of students working on the experiments. We found statistically significant improvement in students' experimental problem-solving skills over the course of a semester. The study also analyzed students' perceptions about the benefits and challenges of the open-ended collaborative lab.