The development of intercultural communicative competence in EFL (English as a Foreign Language) education in many countries is still a difficult goal to achieve. EFL teachers and learners require more tangible and concrete methodological approaches to foster this important competence in the classroom. Therefore, this reflection article aims at proposing the use of genre-based learning as a significant communicative language approach to foster English learners' intercultural communicative competence (ICC) through a Sequence of Critical Thinking Tasks. Through two samples of genres, the article explains how the "skills of discovery," "of interpreting," and "of relating," contained in the concept of ICC, can be articulated, complemented, and enhanced gradually through a set of more specific Critical Thinking Tasks. These mental skills can be useful to help learners understand, discover, interpret, and evaluate critically elements of deep culture that appear in different documents, genres, or texts produced by English-spoken cultures, other language communities, and learners' own culture. Doing critical thinking tasks through genre-based approach can constitute a preliminary but significant step to enhance English learners' critical intercultural awareness in EFL learning environments.