How to Make It
Cut off corn kernels from ears; scrape corn from cobs to yield about 2 cups total. Set aside kernels and scraped corn; discard cobs.
Stir together peas and salt in a medium saucepan. Add water to cover by a depth of 1 inch. Bring to a boil over high, skimming foam that rises to the top. Reduce heat to medium, and partially cover. Simmer until tender, 15 to 25 minutes. Drain; set aside.
While peas simmer, cook ham in a small saucepan over medium, stirring often, until slightly browned, about 5 minutes. Add cream and tomato paste, stirring to loosen browned glaze from bottom of pan. Reduce heat to medium, and bring to a simmer; remove from heat. Set aside.
Melt butter in a large skillet over medium-high. Add onion; cook, stirring occasionally, until onion starts to soften, about 5 minutes. Stir in corn, peas, and okra. Reduce heat to medium-low; cover and cook, undisturbed, 5 minutes. (Let okra cook a few minutes before stirring to reduce stringiness.)
Uncover skillet. Stir in reserved ham-cream mixture, and cook, stirring occasionally, until vegetables are tender and sauce thickens slightly, 10 minutes. Stir in hot sauce and pepper. Stir in basil; serve immediately.