Working over a large bowl, cut kernels off the corn. Scrape the cobs well, using the bowl to reserve the kernels and any juice from the cobs.
Heat oil in a skillet, preferably cast iron, over medium-high heat. Add the chopped onion and sauté, stirring occasionally, until the onion starts to soften, about 4 minutes. Then add the celery and pepper. Continue cooking and stirring until vegetables grow soft and fragrant, about another 5 minutes.
Stir in the jalapeno, grape tomatoes, corn, thyme and smoked paprika. Reduce heat to medium, cover and let the maque choux simmer for 10 minutes. Mixture will throw off liquid, creating its own broth.
Remove lid, add optional chopped greens and stir until greens just wilt. Add chopped fresh basil and season generously with sea salt and fresh ground pepper.