Heat the butter and olive oil in a large skillet over medium heat. In separate sections of the pan, place the onion, bell pepper, okra, cherry tomatoes, and jalapeño, if using. Let cook for 1 minute without touching.

Add the garlic, smoked paprika, thyme, salt, and several grinds of pepper. Stir to combine all the ingredients in the pan. Cook for 4 minutes, stirring occasionally, then add the corn and lima beans and cook for 3 to 5 more minutes, or until softened and heated through.

Remove the thyme sprigs, then stir in the lemon juice and vinegar.

Remove from the heat and stir in the basil. Season to taste and serve.