Recommender systems have long been utilized to provide personalized recommendations based on available datasets and user interactions. However, in data-constrained environments, tailoring recommendations to individual preferences is often challenging. This difficulty is more pronounced when trying to discern user likes and dislikes solely from interaction matrices. This paper conceptualizes a personalized recommender system as a problem of mathematical matrix completion, where missing values in a matrix are predicted using machine learning models. In this work, a novel collaborative filtering model, RecKross, is introduced. RecRoss composes a newly proposed 2D kernel layer to extract latent features and a k-Cross kernel to enhance collaborative filtering capabilities. Through an ablation study, we analyze how model hyperparameters and dataset sparsity (density) impact the performance of RecKross. The proposed model demonstrates promising results on benchmark collaborative filtering datasets and competes favorably with existing models, achieving state-of-the-art performance on datasets, such as, MovieLens and Douban on metrics like RMSE, MAE and NDCG. As RecKross is built to perform in low-data settings, it subsequently shows promising results for the Cold Start problem.