Spread the corn kernels on a baking sheet and roast in the oven for 10-12 minutes, until caramelized and beginning to brown. Keep a careful eye to avoid hardening the kernels. Remove from the oven and set aside.
While the corn is roasting, add lima beans and water to a saucepan. Bring the water to a boil, then reduce to medium heat and cook the lima beans for 7 minutes. Drain the water and set the lima beans aside.
Chop the onions, shallots, bell peppers, garlic, and halve the cherry tomatoes. Set aside the cherry tomatoes for later.
In a large nonstick skillet, sauté the onions, okra, bell peppers, shallots, and garlic on medium heat for 7 minutes, stirring frequently. Add a splash of water, about 1 tsp, if the pan gets too dry.
Add the roasted corn and cooked lima beans to the sautéed vegetables, and cook for an additional 5 minutes, stirring frequently.
Remove the skillet from heat and stir in the halved cherry tomatoes, lime juice, rice vinegar, fresh basil, and smoked paprika.
Cover the skillet with a lid and let the dish rest for 5 minutes to allow the flavors to meld.