Pre-heat oven to 425°F.
Meanwhile, in a medium saucepan, bring 1 cup water to a boil.
Once boiling, add the butter beans and return to a boil; reduce the heat and simmer, covered, until the beans are al dente; about 8 minutes.
Remove from heat, strain, and sprinkle with 1/4 teaspoon kosher salt; set aside.
While the butter beans are cooking, spread the okra in an even layer on a lined baking sheet; drizzle with 1 teaspoon olive oil, and sprinkle with 1/4 teaspoon kosher salt.
Roast the okra for 16 to 18 minutes; remove from the oven; set aside.
Heat a large cast-iron skillet or Dutch oven, over medium heat; add the Andouille sausage and cook until it’s crisp and the fat has rendered.
Remove the sausage with a slotted spoon; set aside.
Add the onion, bell pepper and garlic to the rendered fat in the skillet or Dutch oven, and cook until the vegetables are softened, about 5 minutes.
Add the corn, tomatoes, lima beans, okra, 1 teaspoon kosher salt, 1/2 teaspoon black pepper and Andouille sausage; stir, cover, and cook for about 8 minutes over medium heat.
As vegetables cook, pat the shrimp dry with paper towels, then generously season with 1/2 teaspoon salt and 1/4 teaspoon black pepper.
In a separate large skillet, heat the remaining 1 tablespoon of olive oil over medium-high.
Once the oil is shimmering, add the shrimp in a single layer; cook for 2 minutes, then flip and cook for another 2 to 3 minutes, until pink and cooked through.
Stir the cooked shrimp into the succotash; add the fresh basil and stir.
Taste and adjust seasoning, as needed.
Turn off heat and let sit uncovered for about 5 minutes to let the flavors meld; serve warm.
