Step 1: In a large stockpot or Dutch oven, heat the olive oil over medium-high heat. Add the sliced smoked sausage and cook until nicely browned and slightly crispy, about 5-7 minutes. Remove the sausage with a slotted spoon and set aside, leaving any rendered fat in the pot.
Step 2: Reduce heat to medium. Add the chopped onion to the pot and sauté until softened and translucent, about 5 minutes. Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 3: Pour in the chicken broth and add the bay leaves, lemon slices, and Cajun/Creole seasoning. Bring the mixture to a simmer, scraping up any browned bits from the bottom of the pot.
Step 4: Add the quartered potatoes to the simmering broth. Cook for about 10-12 minutes, or until they are nearly tender. Then, add the corn cobs and continue to cook for another 5-7 minutes, until both are tender-crisp.
Step 5: Reduce the heat to low. Add the melted butter to the pot. Stir gently until fully incorporated, creating a rich, luscious sauce.
Step 6: Return the cooked sausage to the pot. Add the peeled hard-boiled eggs and the shrimp. Stir gently to combine everything, ensuring all components are coated in the glorious sauce. Cook for just 2-3 minutes, or until the shrimp are pink and opaque.
Step 7: Remove the bay leaves and lemon slices. Stir in the fresh parsley and a squeeze of fresh lemon juice, if desired. Taste and adjust seasoning as needed. Serve immediately, perhaps with some crusty bread for soaking up every last drop of that incredible sauce.