Gaining insights into the preferences of new users and subsequently personalizing recommendations necessitate managing user interactions intelligently, namely, posing pertinent questions to elicit valuable information effectively. In this study, our focus is on a specific scenario of the cold-start problem, where the recommendation system lacks adequate user presence or access to other users' data is restricted, obstructing employing user profiling methods utilizing existing data in the system. We employ Active Learning (AL) to solve the addressed problem with the objective of maximizing information acquisition with minimal user effort. AL operates for selecting informative data from a large unlabeled set to inquire an oracle to label them and eventually updating a machine learning (ML) model. We operate AL in an integrated process of unsupervised, semi-supervised, and supervised ML within an explanatory preference elicitation process. It harvests user feedback (given for the system's explanations on the presented items) over informative samples to update an underlying ML model estimating user preferences. The designed user interaction facilitates personalizing the system by incorporating user feedback into the ML model and also enhances user trust by refining the system's explanations on recommendations. We implement the proposed preference elicitation methodology for food recommendation. We conducted human experiments to assess its efficacy in the short term and also experimented with several AL strategies over synthetic user profiles that we created for two food datasets, aiming for long-term performance analysis. The experimental results demonstrate the efficiency of the proposed preference elicitation with limited user-labeled data while also enhancing user trust through accurate explanations.