Kosher salt, ground black pepper, and ground cayenne to taste
6 piping-hot biscuits, for serving
Preheat oven to 450 degrees. Line a baking sheet with nonstick aluminum foil or regular aluminum foil misted with nonstick spray. Arrange ham slices in a single layer. Roast until ham begins to brown, about 5 minutes. Let cool on pan. (The ham will continue to crisp at it cools.)
In a large skillet over medium-high heat, melt butter. When the foam subsides, add onion and a pinch of salt. Cook, stirring often, until onion begins to soften, about 5 minutes. Add garlic and cook until fragrant, about 1 minute.
Stir in okra, corn, and peas. Reduce heat to medium-low, cover, and cook without stirring for 10 minutes. (Letting okra cook for a while before stirring reduces the stringiness from its juices.) Continue cooking, stirring occasionally, until the vegetables are tender, about 5 minutes more.
Stir in basil and enough crème fraîche to make a little sauce. Season generously with salt and pepper and a pinch of cayenne. Keep warm over low heat while biscuits bake.
To serve, split biscuits and place on serving plates. Top each biscuit half with a piece of ham, then spoon warm succotash over top. Serve hot.