I've had great luck direct-sowing Thai basil into my front (non-container) flower/herb/veg garden. IIRC, I held off on sowing until around the first of June, after the daffodils and tulips dad pooped out, and they did a great job of covering the unsightly dying foliage. The combo of good, warm soil and the plentiful rain we had last year provided a solid supply for the entire growing season, both for the usual uses in salads and in cooked Thai dishes, and for a sort of Asian pesto.** The plants that I allowed to flower were quite decorative, and big favorites of the bees. Just don't be tempted to sow yet! Patience is a virtue with hot-weather annuals.
Good luck!
**more of a
pistou - no nuts, no cheese, though the addition of finely chopped macadamias or peanuts would be very tasty. Combine garlic, a couple of Thai or serrano chiles, basil, cilantro, and mint, some kosher salt, and a little bit of turbinado sugar in a processor; drizzle in peanut oil to make a loose paste. Great as a marinade for chicken or pork for grilling, as an addition to noodles (I'd add the chopped nuts for this use), or added to a meat/veg stir-fry; add a slug of fish sauce if you like it, as well as a squeeze of fresh lime juice. Freezes well; use small containers, and put a piece of plastic wrap directly on the surface of the mixture before sealing the container.