Abstract: Quasi-linear convective systems (QLCSs) can produce multiple hazards (e.g., straight-line winds, flash flooding, and mesovortex tornadoes) that pose a significant threat to life and property, and are often difficult to accurately forecast. The NSSL Warn-on-Forecast System (WoFS) is a convection-allowing ensemble system developed to provide short-term, probabilistic forecasting guidance for severe convective events. Examination of WoFS's capability to predict QLCSs has yet to be systematically assessed across a large number of cases for 0-6-hr forecast times. In Part I of this study, the quality of WoFS QLCS forecasts for 50 QLCS days occurring between 2017-2020 is evaluated using object-based verification techniques. First, a storm mode identification and classification algorithm is tuned to identify high-reflectivity, linear convective structures. The algorithm is used to identify convective line objects in WoFS forecasts and Multi-Radar Multi-Sensor system (MRMS) gridded observations. WoFS QLCS objects are matched with MRMS observed objects to generate bulk verification statistics. Results suggest WoFS's QLCS forecasts are skillful with the 3- and 6-hr forecasts having similar probability of detection and false alarm ratio values near 0.59 and 0.34, respectively. The WoFS objects are larger, more intense, and less eccentric than those in MRMS. A novel centerline analysis is performed to evaluate orientation, length, and tortuosity (i.e., curvature) differences, and spatial displacements between observed and predicted convective lines. While no systematic propagation biases are found, WoFS typically has centerlines that are more tortuous and displaced to the northwest of MRMS centerlines, suggesting WoFS may be overforecasting the intensity of the QLCS's rear-inflow jet and northern bookend vortex. One of the most challenging aspects of QLCS prediction is the ability to accurately forecast mesovortex tornado potential. The current paradigm employed by the National Weather Service for forecasting the likelihood that a QLCS will produce a mesovortex and, potentially, a tornado is known as the Three Ingredients Method (3IM). This technique's first two ingredients are grounded in RKW Theory, which states there should be a balance between the strength of the QLCS's cold pool and the magnitude of line-normal shear to produce an optimal balanced state that favors strong, upright updrafts and enhanced low-level rotation. However, mesovortices have been observed despite sub-optimal line-normal shear within the framework of the 3IM. Additionally, observational studies examining prolific mesovortex- and tornado-producing QLCSs found a component of the low-level environmental shear field that was oriented line-parallel, which is not included in the 3IM. Recent observational and modeling work suggest line-parallel shear fosters the development of strong, cyclonic mesovortices, thus increasing the overall likelihood of QLCS tornadoes. Motivated by these recent results, Part II of this study examines three tornadic QLCS case studies from 12 May 2022, 30 March 2022, and 15 December 2021 to investigate the potential of using the upstream kinematic environment to predict QLCS mesovortices in WoFS. Using object-based identification methods and a new technique to isolate the leading line of the WoFS QLCS objects, we are able to calculate the shear components upstream of the QLCS. Results suggest that near-storm shear components can be combined with information about the local line geometry to provide a system-relative forecast of mesovortex tornado potential in WoFS. A new composite parameter, called QTor, characterizes how favorable the environment is for the development of mesovortex tornadoes based on the magnitudes of 0-1-km line-parallel shear, 0-3-km line-normal shear, and the local tortuosity/curvature of the leading line. For each case study, the QTor forecasts are able to predict areas favorable for the development of mesovortex tornadoes that also coincide with the documented tornado reports for each case. However, small orientation differences between the WoFS and MRMS leading lines results in QTor false alarms, which will need to be accounted for and mitigated in the future. The long-term goal of this project is to revise the 3IM and bring it into a more objective framework that can then be implemented into any convection-allowing model.