Melt butter in a large skillet over medium-high heat.
When butter stops foaming, add andouille sausage. Cook, breaking up sausage and stirring occasionally, until lightly browned, 6 to 8 minutes.
Add onion, corn, bell pepper, okra, and garlic. Add thyme leaves. Cook, stirring occasionally until vegetables are softened, 6 to 8 minutes.
Add cream and cayenne; bring mixture to a boil over medium~high heat. Reduce heat to medium. Simmer, stirring occasionally until slightly thickened, 5 to 6 minutes.
Stir in black pepper.