Early experiences in science, technology, engineering, and math (STEM) are important for getting youth interested in STEM fields, particularly for girls. Here, we explore how an after-school robotics club can provide informal STEM experiences that inspire students to engage with STEM in the future. Human-centered robotics, with its emphasis on the social aspects of science and technology, may be especially important for bringing girls into the STEM pipeline. Using a problem-based approach, we designed two robotics challenges. We focus here on the more extended second challenge, in which participants were asked to imagine and build a telepresence robot that would allow others to explore their space from a distance. This research follows four girls as they engage with human-centered telepresence robotics design. We constructed case studies of these target participants to explore their different forms of engagement and phases of interest development--considering facets of behavioral, social, cognitive, and conceptual-to-consequential engagement as well as stages of interest ranging from triggered interest to well-developed individual interest. The results demonstrated that opportunities to personalize their robots and feedback from peers and facilitators were important motivators. We found both explicit and vicarious engagement and varied interest phases in our group of four focus participants. This first iteration of our project demonstrated that human-centered robotics is a promising approach to getting girls interested and engaged in STEM practices. As we design future iterations of our robotics club environment, we must consider how to harness multiple forms of leadership and engagement without marginalizing students with different working preferences.