Producing initial process models currently requires gathering knowledge from multiple process participants and using modeling tools to produce a visual representation. With traditional tools this can require significant effort and thus delay the feedback cycle where the initial model is validated and refined based on participants' feedback. In this paper we aim at reducing the effort required to obtain an initial process model by applying existing process mining techniques to sample process logs obtained directly from process participants. To that end, we specify a simple domain-specific language to represent process log fragments with natural language, and we illustrate the architecture of a live modeling tool, which produces a draft representation of the control flow which is updated in real-time as the logs are written down. The draft models generated by the tool can later be refined and completed by the business analysts using traditional tools. We argue that our synthesis of mining with modeling could provide benefits both in terms of efficiency in generating the initial draft model, as well as in terms of reducing the cognitive load of the business analyst during the requirements gathering phase.