Step 1

Cook sausage and ham in a large pot over medium heat, stirring occasionally, until browned, about 12 minutes; transfer to a plate. Wipe out pot.

Step 2

Melt butter in same pot over medium-high heat. Cook onion, celery, green pepper, red pepper, and 1 tsp. salt, stirring frequently, until onion is translucent, 10–12 minutes. Stir in tomatoes, garlic, jalapeño, tomato paste, and thyme; cook until heated through, about 1 minute. Season with salt.

Step 3

Add chicken stock and bring to a boil. Stir in rice, bay leaves, and hot sauce. Season with salt and pepper.

Step 4

Return to a boil, then reduce heat to low and simmer, covered, 15 minutes. Uncover and stir in reserved sausage and ham. Cook until heated through, about 5 more minutes.

Step 5

Add shrimp, scallions, and ¼ cup parsley. Stir a few times to allow shrimp to begin cooking, then cover pot, turn off heat, and let jambalaya sit until shrimp are cooked through, 15–18 minutes. Transfer to a large bowl, then top with remaining ¼ cup parsley. Serve with lemon wedges alongside.