Common basil is a plant with high environmental requirements and is of great importance both in amateur and large-scale cultivation. One method of obtaining fresh basil is container cultivation. The study aimed to determine the feasibility of growing Greek basil in autumn under temperate climate conditions in containers with diameters of 9, 10, and 11 cm, under cover (polytunnel and unheated greenhouse), as well as in the risky field cultivation due to the risk of frost. The highest yield (23.8 g·plant−1) was obtained in greenhouse cultivation in the smallest containers. The plants growing in the greenhouse were characterized by the highest content of chlorophyll a (72.77 mg·100 g−1 FW), chlorophyll a + b (105.1 mg·100 g−1 FW), and carotenoids (20.87 mg·100 g−1 FW). Fifty-three compounds of basil essential oil were identified and characterized, with growth conditions (location/pot) modifying its chemical composition. The highest essential oil content (0.30%) was found in plants grown in the greenhouse in the largest pots. Methyl eugenol (35.96–69.85%) and eugenol (7.29–28.12%) dominated in the tested essential oil, followed by linalool (1.90–9.77%), α-trans-bergamotene (3.78–7.20%), (E)-β-farnesene (2.39–3.74%), and 1,8-cineole (1.49–5.22%). The conducted studies confirm the possibility of harvesting aromatic basil raw material rich in biocomponents from autumn cultivation in containers in the field and under cover.